Twisted Patterns Research Articles

Acoustic materials based on the Gosper curve

In this work, slotted acoustic materials based on a space filling curve called the Peano-Gosper curve are proposed and investigated. The slits in such materials form a complex pattern because they are divided by walls built along lines generated by the Gosper curve algorithm. The pattern can be twisted around an axis normal to its surface to increase the tortuosity inside the material, and therefore, modify its acoustic properties, which can be controlled by the turning angle or pitch of the twist. A highly efficient semi-analytical model has been developed to accurately predict the acoustic properties, in particular the sound absorption of such materials. It only requires a representative part of the pattern, or better, scanning the surface of the fabricated material so that the actual geometry and dimensions (in particular slit widths) are well reproduced in a two-dimensional finite element mesh generated on a representative fluid domain. The mesh is used to solve a dedicated Poisson problem and determine a few key parameters, and the rest of the modelling is based on analytical formulas. Material samples with straight and twisted slit patterns were 3D printed and then measured in an impedance tube to confirm semi-analytical sound absorption predictions.

Competition between drift and topological transport of colloidal particles in twisted magnetic patterns

We simulate the motion of paramagnetic particles between two magnetic patterns with hexagonal symmetry that are twisted at a magic angle. The resulting Morié pattern develops flat channels in the magnetic potential along which colloidal particles can be transported via a drift force of magnitude larger than a critical value. Colloidal transport is also possible via modulation loops of a uniform external field with time varying orientation, in which case the transport is topologically protected. Drift and topological transport compete or cooperate giving rise to several transport modes. Cooperation makes it possible to move particles at drift forces weaker than the critical force. At supercritical drift forces the competition between the transport modes results e.g. in an increase of the average speed of the particles in integer steps and in the occurrence of subharmonic responses. We characterize the system with a dynamical phase diagram of the average particle speed as a function of the direction of the topological transport and the magnitude of the drift force.

Disorder scattering in classical flat channel transport of particles between twisted magnetic square patterns

We measure the trajectories of macroscopic magnetic particles pulled against gravity between twisted alternating magnetic square patterns in a superposed homogeneous magnetic field normal to both patterns. The two patterns are built from a set of magentic cubes having a distribution of magnetization. The magnetic potential between the patterns is a sum of three contributions: two being periodic on two lattices with different magnitude and orientation, and the third random contribution arising from the distribution of magnetization of the cubes. As one varies the twist angle between the two patterns each time the twist angle coincides with a magic twist angle one of the two periodic lattices becomes a sublattice of the other lattice. Simulations of particles moving through patterns with a precise cube magnetization produce pronounced mobility peaks near magic twist angles that are associated with flat channels. Weak random fluctuations of the cube magnetization in the experiment and the simulations cause enhanced random disorder of the potential and reduce the mobility by scattering particles into the interior of the twisted Wigner Seitz cells. The mobility undergoes an Anderson transition from magic to generic behavior as the magnetization disorder increases beyond half of a percent of the cube magnetization.

Numerical study of mixing performance in T-junction passive micromixer with twisted design

In this study, numerical computations are performed with the main purpose of shedding light on the mixing characteristics in an innovative T-shaped micromixer equipped with a twisted structure. A 3-D model is presented and verified to mix two miscible fluids in a single phase. By considering different geometrical cases, the proposed T-mixer is compared using the standard T-mixer (Base case) running in the same operational conditions. Furthermore, the impacts of variation in the geometry of twisted design are scrutinized for Re (Reynolds number) in the extent of 1≤Re≤500 with the focus of obtaining a significant mixing quality for flow through the micromixer. MI (Mixing index), PI (performance index), and pressure drop are evaluated for micromixers with and without twisted patterns considering various values of Reynolds number. The numerical outcomes demonstrate that the MI (mixing performance) and PI (performance index) improve remarkably for T-shaped microchannel with twisted patterns, particularly Re`=200, due to the geometry of the curvature and the presence of secondary flow in the mixer. It is also found that case 6 yields the greatest improvement in mixing implementation by increasing the mixing index up to 142 percent.

Moiré metasurfaces for dynamic beamforming.

Recent advances in digitally programmable metamaterials have accelerated the development of reconfigurable intelligent surfaces (RIS). However, the excessive use of active components (e.g., pin diodes and varactor diodes) leads to high costs, especially for those operating at millimeter-wave frequencies, impeding their large-scale deployments in RIS. Here, we introduce an entirely different approach—moiré metasurfaces—to implement dynamic beamforming through mutual twists of two closely stacked metasurfaces. The superposition of two high-spatial-frequency patterns produces a low-spatial-frequency moiré pattern through the moiré effect, which provides the surface impedance profiles to generate desired radiation patterns. We demonstrate experimentally that the direction of the radiated beams can continuously sweep over the entire reflection space along predesigned trajectories by simply adjusting the twist angle and the overall orientation. Our work opens previously unexplored directions for synthesizing far-field scattering through the direct contact of mutually twisted metallic patterns with different plane symmetry groups.

The Seasonality of Surface Urban Heat Islands across Climates

In this work, we investigate how the seasonal hysteresis of the Surface Urban Heat Island Intensity (SUHII) differs across climates and provide a detailed typology of the daytime and nighttime SUHII hysteresis loops. Instead of the typical tropical/dry/temperate/continental grouping, we describe Earth’s climate using the Köppen–Geiger system that empirically maps Earth’s biome distribution into 30 climate classes. Our thesis is that aggregating multi-city data without considering the biome of each city results in temporal means that fail to reflect the actual SUHII characteristics. This is because the SUHII is a function of both urban and rural features and the phenology of the rural surroundings can differ considerably between cities, even in the same climate zone. Our investigation covers all the densely populated areas of Earth and uses 18 years (2000–2018) of land surface temperature and land cover data from the European Space Agency’s Climate Change Initiative. Our findings show that, in addition to concave-up and -down shapes, the seasonal hysteresis of the SUHII also exhibits twisted, flat, and triangle-like patterns. They also suggest that, in wet climates, the daytime SUHII hysteresis is almost universally concave-up, but they paint a more complex picture for cities in dry climates.

Enhanced colloidal transport in twisted magnetic patterns

Bilayers of two-dimensional materials twisted at specific angles can exhibit exceptional properties such as the occurrence of unconventional superconductivity in twisted graphene. We demonstrate here that novel phenomena in twisted materials emerges also in particle-based classical systems. We study the transport of magnetic colloidal particles driven by a drift force and located between two twisted periodic magnetic patterns with either hexagonal or square symmetry. The magnetic potential generated by patterns twisted at specific magic angles develops flat channels, which increase the mobility of the colloidal particles compared to that in single patterns. We characterize the effect of the temperature and that of the magnitude of the drift force on the colloidal mobility. The transport is more enhanced in square than in hexagonal twisted patterns. Our work extends twistronics to classical soft matter systems with potential applications to lab-on-a-chip devices.

Compact Topology-Aware Bus Routing for Design Regularity

In bus routing, if signal bits in a bus structure share a common routing topology, routability is increased by avoiding twisted patterns and variation immunity. The bus routing problem has become significantly important because of increasing complexity of bus structures for multichip-module, I/O pins, or on-chip memories in advanced technology. We present and evaluate a compact topology-aware bus routing method that can both compactly synthesize the routing topology of the bus and minimize design rule violations even in designs with high bus density and high track utilization. Our proposed method completed the bus routing in the runtime limit of the ICCAD-2018 contest and achieved 66% reduction in total cost compared with the winner of that contest.

Binary square axicon with chiral focusing properties for optical trapping

We introduce a novel phase-only diffractive optical element called chiral binary square axicon (CBSA). The CBSA is designed by linearly rotating the square half-period zones of the binary square axicon with respect to one another. A quadratic phase mask (QPM) is combined with the CBSA using modulo-2{\pi} phase addition technique to bring the far-field intensity pattern of CBSA at the focal plane of the QPM and to introduce quasi-achromatic effects. The periodically rotated zones of CBSA produces a whirlpool phase profile and twisted intensity patterns at the focal plane of QPM. The degree of twisting seen in the intensity patterns is dependent upon the angular step size of rotation of the zones. The intensity pattern was found to rotate around the optical axis along the direction of propagation. The phase patterns of CBSA with different angles of zone rotation are displayed on a phase-only spatial light modulator and the experimental results were found to match with the simulation results. To evaluate the optical trapping capabilities of CBSA, an optical trapping experiment was carried out and the optical fields generated by CBSA were used for trapping and rotating yeast cells.

Twisted patterns in large subsets of $\mathbb Z^N$

Let E \subset \mathbb Z^N be a set of positive upper Banach density, and let \Gamma < \mathrm {GL}_N(\mathbb Z) be a "sufficiently large" subgroup. We show in this paper that for each positive integer m there exists a positive integer k with the following property: For every \{a_1,\ldots,a_m\} \subset k \cdot \mathbb Z^N , there are \gamma_1,\ldots,\gamma_m \in \Gamma and b \in E such that \gamma_i \cdot a_i \in E - b, \quad \text{for all $i = 1,\ldots,m$}. We use this „twisted" multiple recurrence result to study images of E-b under various \Gamma -invariant maps. For instance, if N \geq 3 and Q is an integer quadratic form on \mathbb Z^N of signature (p,q) with p,q \geq 1 and p + q \geq 3 , then our twisted multiple recurrence theorem applied to the group \Gamma = \mathrm {SO}(Q)(\mathbb Z) shows that k^2 Q(F) \subset Q(E-b), for every F \subset k \cdot \mathbb Z^N with m elements. In the case when E is an aperiodic Bohr _o set, we can choose b to be zero and k = 1 , and thus Q(\mathbb Z^N) \subset Q(E) . Our result is derived from a non-conventional ergodic theorem which should be of independent interest. Important ingredients in our proofs are the recent breakthroughs by Benoist–Quint and Bourgain–Furman–Lindenstrauss–Mozes on equidistribution of random walks on automorphism groups of tori.

Clinical characteristics of narrow-band imaging of oral erythroplakia and its correlation with pathology.

BackgroundTo analyze the clinical application of endoscope with narrow-band imaging (NBI) system in detecting high-grade dysplasia, carcinoma in situ, and carcinoma in oral erythroplakia.MethodsThe demographic, histopathological data, and NBI vasculature architectures of patients receiving surgical intervention for oral erythroplakia were retrospectively reviewed and analyzed statistically.ResultsA total of 72 patients, including 66 males and 6 females, with mean age of 54.6 ± 11.2 years, were enrolled. The odds ratio of detecting high-grade dysplasia, carcinoma in situ, and carcinoma by twisted elongated morphology and destructive pattern of intraepithelial microvasculature was 15.46 (confidence interval 95 %: 3.81–72.84), and the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were 80.95 %, 78.43 %, 60.71 %, 90.91 %, and 79.17 %, respectively, which were significantly better than other two established NBI criteria (p < 0.001).ConclusionsTwisted, elongated, and destructive patterns of intraepithelial papillary capillary loop of NBI images are indicators for high-grade dysplasia, carcinoma in situ, and invasive carcinoma in oral erythroplakia.

Metamaterial with negative index due to chirality

Recently it has been predicted that materials with exceptionally strong optical activity may also possess a negative refractive index, allowing the realization of superlenses for super-resolution imaging and data storage applications. Here we demonstrate experimentally and numerically that a chirality-induced negative index of refraction is possible. A negative index of refraction due to three-dimensional chirality is demonstrated for a bilayered metamaterial based on pairs of mutually twisted planar metal patterns in parallel planes, which also shows negative electric and magnetic responses and exceptionally strong optical activity and circular dichroism. Multilayered forms of the metamaterial are found to be suitable for use as ultrathin polarization rotators and circular polarizers for practical applications.

Self-Organized Swelling of a Metal-Capped Polymer Thin Bilayer

We report on the formation of self-organized surface patterns on a thin metal film capped polymer bilayer on a substrate by swelling. The self-organization is directed by a periodically corrugated elastomeric mold which exerts a nodal effect that confines the intrinsic swelling wave, and the resulting self-organized patterns are anisotropic and quite periodic. The corrugated pattern confined by the elastomeric mold was observed from the earlier stages of swelling while the small wrinkles (the first self-organized pattern) were formed in the later stages of the swelling. The temporal evolution of the first self-organized pattern was analyzed theoretically on the basis of the wave interaction relationship between the intrinsic swelling wave and the periodic corrugation formed in the earlier stages, and the experimental data were well-matched with the results of the analysis. The maximum value of the harmonic number for the wave number of the corrugated pattern was also analyzed. The strain in the metal thin film increases with increasing swelling time and arrives at a state of mechanical equilibrium (strain growth rate ∼0). The growth rate and moment of arrival of the strain at the state of mechanical equilibrium were different for the metal films on the ridge and groove of the corrugated pattern. In the case of the self-organized swelling directed by a periodically corrugated elastomeric mold with a relatively large line width, irregular wrinkles or twisted patterns (the second self-organized pattern) were observed which were easily distinguished from the corrugated patterns by the pattern replication and the first self-organized swelling patterns.

Use of purified endopolygalacturonase for a topochemical study of elongating cell walls at the ultrastructural level

Endopolygalacturonase, a fungal enzyme purified by Albersheim and his group which specifically degrades the galacturonosyl linkages of pectic polysaccharides, was used at the ultrastructural level on intact tissues from differentiated organs. Specimens were taken from the elongating zone of mung bean (Vigna radiata) hypocotyls. Incubation with the enzyme solution was performed en bloc, prior to embedding and to ultrastructural cytochemistry (PATAg test for polysaccharides), or by flotation of ultrathin frozen sections. From the morphological viewpoint, the images obtained are sharp and reproducible. They support the plywood model for the organization of expanding walls. The ordering of walls appears to be built up very early, at the very beginning of elongation, in the upper part of the hypocotyl (hook). The specificity of the enzyme allows a topochemical study of the wall. Data indicate an uneven distribution of polysaccharides of pectic type across a single wall and among the different cells. Outer and inner wall areas are highly resistant to extraction by endopolygalacturonase. In the middle lamella the insolubility of amorphous components probably indicates a local concentration of highly methyl-esterified carboxyl groups not susceptible to endopolygalacturonase attack; conversely, adjacent parts of the middle lamella are regularly extracted, indicating a high concentration of galacturonans. An intense extraction occurs in the bow-shaped zone, revealing the occurrence of a massive embedding of unesterified pectic polysaccharides around the fibrillar subunits responsible for the twisted patterns. In the inner and recent part of the wall, the ordering of fibrillar subunits seems progressive and possibly related to the peptic embedding. This incrusting material could play a role in the morphogenesis of the ordered wall by means of specific assembly and interconnections of wall subunits.

On the interpretation of twisted patterns in elongating plant cell wall: Informations obtained with ultracryotomy

Ultracryotomy, which gives anin situ visualization of wall subunits, was used to study the texture of elongating wall of mung bean hypocotyl (Phaseolus aureus). The criss-crossed texture of the wall was confirmed. The controversed disposition of the subunits in twisted patterns was analyzed on the basis of observations of oblique sections on which a mild extraction may be performed. Despite the twisted appearance within one sectioning plane, no curved subunits were seen running between the criss-crossed layers. The results confirmed that the appearance of arcs is an illusion due to thin sectioning of successive strata in which the orientation of subunits rotates.

Distortion of Twisted Orientation Patterns in Liquid Crystals by Magnetic Fields

Abstract At rest between parallel plates, cholesteric liquid crystals commonly exhibit a characteristic twisted orientation pattern, the axis of twist being perpendicular to the plates. Also, this orientation pattern appears possible in nematic liquid crystals, since it is consistent with continuum theory(1) for both types of liquid crystal. This paper discusses the influence upon such a twisted orientation pattern of a magnetic field perpendicular to the plates. If one employs a free energy of the form discussed by Frank,(2) the continuum theory equations have solutions relevant to this situation. For nematic liquid crystals, provided that the twist is not too large, our analysis suggests that no distortion of the orientation pattern occurs until the magnetic field strength exceeds a critical value which varies with the amount of twist. For cholesteric liquid crystals, there seems to be two possibilities depending upon the relative magnitudes of two Frank constants. Either distortion always occurs above a critical field strength, or does so only when the distance between the plates is sufficiently small.

Stability of Orientation Patterns of Liquid Crystals Subject to Magnetic Fields

Previous article Next article Stability of Orientation Patterns of Liquid Crystals Subject to Magnetic FieldsConstantine M. DafermosConstantine M. Dafermoshttps://doi.org/10.1137/0116109PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] F. C. Frank, On the theory of liquid crystals, Discussions Faraday Soc., 25 (1958), 19–28 10.1039/df9582500019 CrossrefGoogle Scholar[2] A. Saupe, Die Biegungselastizität der nematischen Phase von Azoxyanisol, Z. Naturforsch., 15a (1960), 815–822 Google Scholar[3] J. L. Ericksen, Continuum theory of liquid crystals, Appl. Mech. Rev., 20 (1967), 1029–1032 Google Scholar[4] Charles B. Morrey, Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966ix+506 MR0202511 0142.38701 CrossrefGoogle Scholar[5] R. Courant and , D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953xv+561 MR0065391 0053.02805 Google Scholar[6] W. F. Osgood, On the existence of a minimum of the integral $\int\sp {x\sb 1}\sb {x\sb 0}F(x,y,y')dx$ when $x\sb 0$ and $x\sb 1$ are conjugate points, and the geodesics on an ellipsoid of revolution: a revision of a theorem of Kneser's, Trans. Amer. Math. Soc., 2 (1901), 166–182 MR1500563 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The Freedericksz transition as a bifurcation problemDynamics and Stability of Systems, Vol. 14, No. 3 | 1 Sep 1999 Cross Ref The effect of splay-bend elasticity on Freedericksz transitions in an annulusLiquid Crystals, Vol. 26, No. 5 | 1 May 1999 Cross Ref Weak-anchoring effects on a Freedericksz transition in an annulusLiquid Crystals, Vol. 19, No. 1 | 24 September 2006 Cross Ref InstabilitiesVariational Theories for Liquid Crystals | 1 Jan 1994 Cross Ref Response of a twisted nematic liquid crystal to any applied potentialLiquid Crystals, Vol. 4, No. 2 | 1 Feb 1989 Cross Ref Bénard convection in liquid crystalsLiquid Crystals, Vol. 4, No. 3 | 1 Jan 1989 Cross Ref On the Variation of the K 13 Nematic Surface-Like Volume Energy and the Nematic Surface Energy of MadaMolecular Crystals and Liquid Crystals, Vol. 148, No. 1 | 13 December 2006 Cross Ref Some Topics in Equilibrium Theory of Liquid CrystalsTheory and Applications of Liquid Crystals | 1 Jan 1987 Cross Ref Optical study of the molecular alignment in a nematic liquid crystal in an oblique magnetic fieldJournal de Physique, Vol. 45, No. 2 | 1 Jan 1984 Cross Ref Anisotropic FluidsTheories of Fluids with Microstructure | 1 Jan 1984 Cross Ref Some bifurcation problems in cholesteric liquid crystal theoryProceedings of the Edinburgh Mathematical Society, Vol. 26, No. 3 | 20 January 2009 Cross Ref Twofold orientations and hysteresis properties of nematic liquid crystals in strong magnetic fieldsJournal of Applied Physics, Vol. 50, No. 5 | 1 May 1979 Cross Ref Theoretical investigation of Freedericksz transitions in twisted nematics with surface tiltJournal of Physics A: Mathematical and General, Vol. 11, No. 7 | 18 January 2001 Cross Ref Polar flexoelectric deformations and second order elasticity in nematic liquid crystalsJournal de Physique, Vol. 38, No. 8 | 1 Jan 1977 Cross Ref Equilibrium Theory of Liquid CrystalsAdvances in Liquid Crystals | 1 Jan 1976 Cross Ref Physics of liquid crystalsReviews of Modern Physics, Vol. 46, No. 4 | 1 October 1974 Cross Ref Dependence of birefringence threshold voltage on dielectric anisotropy in a nematic liquid crystalJournal of Applied Physics, Vol. 45, No. 8 | 1 Aug 1974 Cross Ref Applications of microcontinuum fluid mechanicsInternational Journal of Engineering Science, Vol. 12, No. 4 | 1 Apr 1974 Cross Ref Interfacial effects in the magnetohydrostatic theory of nematic liquid crystalsJournal of Physics A: Mathematical, Nuclear and General, Vol. 6, No. 6 | 15 March 2001 Cross Ref Some Features of a Continuum Description of Disclination Lines in Nematic Liquid CrystalsMolecular Crystals and Liquid Crystals, Vol. 24, No. 3-4 | 21 March 2007 Cross Ref Distortion of Twisted Orientation Patterns in Liquid Crystals by Magnetic FieldsMolecular Crystals and Liquid Crystals, Vol. 12, No. 1 | 21 March 2007 Cross Ref Some magneto-hydrostatic effects in nematic liquid crystalsJournal of Physics D: Applied Physics, Vol. 3, No. 6 | 14 May 2002 Cross Ref Couette flow of a nematic liquid crystal in the presence of a magnetic fieldArchive for Rational Mechanics and Analysis, Vol. 37, No. 3 | 1 Jan 1970 Cross Ref Volume 16, Issue 6| 1968SIAM Journal on Applied Mathematics1123-1403 History Submitted:26 March 1968Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116109Article page range:pp. 1305-1318ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Short Report on the Shimmeiyama Site

The small excavation of the Shimmeiyama Site, a prehistoric one in Musashi, yielded 376 potsherds and 4 stone artefacts. Potsherds were of the Early Jomon type, and three patterns of design were identified among them except for those with no decoration ; twisted cord patterns, cord patterns proper and incised patterns. Stone implements are all polished. Chronological situation of the site is not yet determined.

On the Excavation of Fumonji Site, Tochigi Prefecture

The site called Fumonji, Tochigi Pref., lies in the Suburbs of Kiryu City. Our digging work was made in the period from Feb. 20 to Mar 5, 1948. At 60-80cm deep underground were inbedded the most early type of Jomon Pottery sherds and above these, namely in the middle or upper layer we also found three different parts of a dwelling dug in the Loam, probably of the Moroiso type. More than three thousands pieces intact or broken pebbeles, half or full worked stone implements and sherds of pottery were collected separately from the all eighteen 2-meters squares and 4 layers representing each main part of the site.Stone used for these implements as materials, are mainly identified to be Palaeozoic sedimentary rocks, such as chert for blade tools, sandstone for axes, and igneous rocks, such as obsidian for arrowpoints, andesite and basalt for axes and hammer stone, etc. Technically remarkable points with these is that only angular flakes were produced, and marginal chipping is all dominant. Sometimes polishing and sawing are witnessed given for axes. The types and forms are classified as follows (see Fig. 2) :Miscellaneous pebbles and boulders unclassificable as artifacts 980Cores utilized for the production of angular flakes 65Raw angular flakes of small and medium size 681Apparently utilized angular flakes 33Flakes with more or less chipped margins 32Flakes with marginal chipping 9Arrow points and spear heads 30Axes 15Potteries of the earliest Jomon types are presented : 1) A simple type with no pattern. 2) A type of twisted cord patterns. 3) Sherds with roll-stamped patterns. 4) Mito type. 5) Upper Tado type. 6) Lower Tado type. 7) Shiboguchi type. 8) Kayama type. Generally speaking roll-stamped patters, Kayama, Kurohama and Moroiso-types form the principal part of the whole materials (see Table 3 & 4).Of the earlier Jomon type are found : 1) Lower Hanazumi type. 2) Sekiyama type. 3) Kurohama type. 4) Moroiso type. The sherds of middle and later Jomon types and Yayoi types are rarely to be found.