Single Twist Research Articles

Invisible Knots and Rainbow Rings: Knots Not Determined by Their Determinants

SummaryWe determine p-colorability of the paradromic rings. These rings arise by generalizing the experiment of bisecting a Möbius strip. Instead of joining the ends with a single half twist, use m half twists, and, rather than bisecting (n = 2), cut the strip into n sections. Replacing each thin strip with its midline results in the m, n paradromic link. Using the notion of p-colorability from knot theory, we determine, for each m and n, which primes p can be used to color the link. Amazingly, almost all admit 0, 1, or an infinite number of prime colorings! This is reminiscent of solutions sets in linear algebra. Indeed, the problem quickly turns into a study of the eigenvalues of a large, nearly diagonal matrix.

An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas.

We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the nonzero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over Ns twist angles from Ns CCD calculations to Ns MP2 calculations plus one CCD calculation.

Collecting Hair Samples for Hair Cortisol Analysis in African Americans.

The hormone cortisol is typically assessed in saliva, serum, or urine samples. More recently, cortisol has been successfully extracted from hair, including humans. The advantage of hair cortisol concentration is that it reflects a retrospective representation of hypothalamic-pituitary-adrenal (HPA) axis function over time, much like hemoglobin A1C represents glycemic control. However, obtaining hair samples can be challenging, due to the cultural beliefs and hair care practices of minority participants. For example, African Americans may be reluctant to provide samples. Additionally, few researchers are trained to collect hair samples from African Americans. The purpose of this paper is to present a culturally informed protocol to help researchers obtain hair samples from African Americans. To illustrate the representative results of this protocol implementation, de-identified data from African Americans that participated in a community-based study on chronic stress are provided. Hair practice preferences are assessed. The participants are made comfortable by showing pictures of hair samples prior to cutting their hair. The single strain twist and gently pull method is used to collect approximately 30 - 50 strands of hair from the posterior vertex region of the scalp. This protocol will significantly improve collection of hair samples from African Americans.

Structure–property of DREF-3 friction spun yarn made using twisted staple fibrous core

ABSTRACTThis article discusses the structure–property relationship of DREF-3 friction spun cotton yarn in which the core is a single twisted cotton ring yarn and the sheath is made of the same cotton fibers. The structural changes in the single staple fiber yarn when subjected to DREF spinning have been studied by using tracer fibers. The single yarn physical properties, namely its count, twist multiplier and twist direction, and the proportion of the sheath fibers used during the spinning trials, were found to correlate with the final Dref yarn mechanical properties. It was observed that the direction of single yarn twist has the most significant effect; besides, the amount of twist multiplier in the single yarn and the proportion of sheath wrapping fibers largely determine the tensile properties of such core yarns. Since breaking tenacity and elongation of the DREF yarn are inversely related, it will be appropriate to compare them in terms of specific work of rupture.

Design of twisted tape turbulator at different entrance angle for heat transfer enhancement in a solar heater

Numerical investigation of heat transfer characteristics in a tube fitted with inserted twisted tape swirl generator is performed. The twisted tapes are separately inserted from the tube wall. The configuration parameters include the, entrance angle (α) and pitch (H). Investigations have been done in the range of α=180°, 160° and 140° with Reynolds number varying between 100 and 20,000. In this paper, transition – SST model which can predict the transition of flow regime from laminar through intermittent to turbulent has been utilized for numerical simulations. The computational results are in good agreement with experimental data. The results show that higher entrance angle yields a higher heat transfer value. The using of single twist twisted tape supplies considerable increase on heat transfer and pressure drop when compared with the conventional twisted tapes. A large data set has been generated for heat transfer and thermal-hydraulic performance which is useful for the design of solar thermal heaters and heat exchangers.

Untwisting information from Heegaard Floer homology

The unknotting number of a knot is the minimum number of crossings one must change to turn that knot into the unknot. We work with a generalization of unknotting number due to Mathieu-Domergue, which we call the untwisting number. The p-untwisting number is the minimum number (over all diagrams of a knot) of full twists on at most 2p strands of a knot, with half of the strands oriented in each direction, necessary to transform that knot into the unknot. In previous work, we showed that the unknotting and untwisting numbers can be arbitrarily different. In this paper, we show that a common route for obstructing low unknotting number, the Montesinos trick, does not generalize to the untwisting number. However, we use a different approach to get conditions on the Heegaard Floer correction terms of the branched double cover of a knot with untwisting number one. This allows us to obstruct several 10 and 11-crossing knots from being unknotted by a single positive or negative twist. We also use the Ozsv\'ath-Szab\'o tau invariant and the Rasmussen s invariant to differentiate between the p- and q-untwisting numbers for certain p,q > 1.

Essential twisted surfaces in alternating link complements

Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement.

Conformational Switching of Multi‐Responsive Ferrocenyl‐Phenol Conjugates

Multifunctional conformational switches based on the ferrocenyl‐salicylic acid amide motif with increasing additional complexity at the Fc moiety (R = COOMe, CONHEt, CONHFc; H‐2–H‐4; Fc = ferrocenyl) have been prepared and their preferred secondary structures in solution have been elucidated by NMR and IR spectroscopy in combination with conformational searches based on DFT calculations. Their distinct conformational responses to deprotonation ([2]––[4]–) and oxidation ([H‐2]+·–[H‐4]+·) have been revealed by IR, EPR, and UV/Vis spectroscopy as well as by DFT calculations. Deprotonation inverts all amide units (double amide twist) whereas oxidation selectively flips the terminal amide unit (single amide twist). The combined action of deprotonation and oxidation has also been explored.

Expression of the prospective mesoderm genes twist, snail, and mef2 in penaeid shrimp.

In penaeid shrimp, mesoderm forms from two sources: naupliar mesoderm founder cells, which invaginate during gastrulation, and posterior mesodermal stem cells called mesoteloblasts, which undergo characteristic teloblastic divisions. The primordial mesoteloblast descends from the ventral mesendoblast, which arrests in cell division at the 32-cell stage and ingresses with its sister dorsal mesendoblast prior to naupliar mesoderm invagination. The naupliar mesoderm forms the muscles of the naupliar appendages (first and second antennae and mandibles), while the mesoteloblasts form the mesoderm, including the muscles, of subsequently formed posterior segments. To better understand the mechanism of mesoderm and muscle formation in penaeid shrimp, twist, snail, and mef2 cDNAs were identified from transcriptomes of Penaeus vannamei, P. japonicus, P. chinensis, and P. monodon. A single Twist ortholog was found, with strong inferred amino acid conservation across all three species. Multiple Snail protein variants were detected, which clustered in a phylogenetic tree with other decapod crustacean Snail sequences. Two closely-related mef2 variants were found in P. vannamei. The developmental mRNA expression of these genes was studied by qPCR in P. vannamei embryos, larvae, and postlarvae. Expression of Pv-twist and Pv-snail began during the limb bud stage and continued through larval stages to the postlarva. Surprisingly, Pv-mef2 expression was found in all stages from the zygote to the postlarva, with the highest expression in the limb bud and protozoeal stages. The results add comparative data on the development of anterior and posterior mesoderm in malacostracan crustaceans, and should stimulate further studies on mesoderm and muscle development in penaeid shrimp.

Second order effect of twist deformations in the D1D5 CFT

Thermalization in the D1D5 CFT should occur via interactions caused by the twist operator, which deforms the theory off its free orbifold point. Earlier studies investigating this deformation at first order did not show any definite evidence of thermalization. In this paper we study the deformation to second order, where we do expect to see the effects that should give thermalization. We compute the effect of two twist operators on an initial vacuum state, which generates a squeezed state analogous to the case for a single twist. We obtain expressions for the Bogoliubov coefficients in this 2-twist case.

Interfacial Atomic Structure of Twisted Few-Layer Graphene

A twist in bi- or few-layer graphene breaks the local symmetry, introducing a number of intriguing physical properties such as opening new bandgaps. Therefore, determining the twisted atomic structure is critical to understanding and controlling the functional properties of graphene. Combining low-angle annular dark-field electron microscopy with image simulations, we directly determine the atomic structure of twisted few-layer graphene in terms of a moiré superstructure which is parameterized by a single twist angle and lattice constant. This method is shown to be a powerful tool for accurately determining the atomic structure of two-dimensional materials such as graphene, even in the presence of experimental errors. Using coincidence-site-lattice and displacement-shift-complete theories, we show that the in-plane translation state between layers is not a significant structure parameter, explaining why the present method is adequate not only for bilayer graphene but also a few-layered twisted graphene.

Raman and infrared spectroscopic studies of structure and stability of 1,1,2,2-tetrachloro-1,3-disilacyclopentane

Raman spectra of liquid, and infrared spectra of gaseous as well as matrix isolated 1,1,2,2-tetrachloro-1,3-disilacyclopentane were recorded and analyzed with the aid of DFT calculations. Complete assignment of the experimental vibrational spectral bands is made. Experimental results and DFT calculations confirm that 1,1,2,2-tetrachloro-1,3-disilacyclopentane exists as single twist conformer in gaseous and liquid states as well as isolated in Ar and N2 matrices. Fast dissociation of 1,1,2,2-tetrachloro-1,3-disilacyclopentane takes place in gas phase, while the molecule remains stabile in condensed phase. The spectral data and results of DFT calculations in anharmonic approximation confirm that dissociation of 1,1,2,2-tetrachloro-1,3-disilacyclopentane starts with the cleavage of CC bond of the five membered ring. Dichlorodimethylsilane and HCl were found to be the main products of the dissociation. The geometry and stability of the title molecule is discussed in the light of recent publications on the studies of similar substituted disilacyclapentanes.

Bulk elastic waves with unidirectional backscattering-immune topological states in a time-dependent superlattice

Recent progress in electronic and electromagnetic topological insulators has led to the demonstration of one way propagation of electron and photon edge states and the possibility of immunity to backscattering by edge defects. Unfortunately, such topologically protected propagation of waves in the bulk of a material has not been observed. We show, in the case of sound/elastic waves, that bulk waves with unidirectional backscattering-immune topological states can be observed in a time-dependent elastic superlattice. The superlattice is realized via spatial and temporal modulation of the stiffness of an elastic material. Bulk elastic waves in this superlattice are supported by a manifold in momentum space with the topology of a single twist Möbius strip. Our results demonstrate the possibility of attaining one way transport and immunity to scattering of bulk elastic waves.

Invariants of the k-fold adjoint action of the Euclidean isometry group

A non-zero element of the Lie algebra \({\mathfrak{se}(3)}\) of the special Euclidean spatial isometry group SE(3) is known as a twist and the corresponding element of the projective Lie algebra is termed a screw. Either can be used to describe a one-degree-of-freedom joint between rigid components in a mechanical device or robot manipulator. This leads to a practical interest in multiple twists or screws, describing the overall instantaneous motion of such a device. In this paper, invariants of multiple twists under the action induced by the adjoint action of the group are determined. The ring of the polynomial invariants for the adjoint action of SE(3) acting on a single twist is well known to be finitely generated by the Klein and Killing forms, while a theorem of Panyushev (Publ. Res. Inst. Math. Sci. 4:1199–1257, 2007) gives finite generation for the real invariants of the induced action on two twists. However we are not aware of a corresponding theorem for k twists, where \({k\geq3}\). Following Study, Geometrie der Dynamen, (1903), we use the principle of transference to determine fundamental algebraic invariants and their syzygies. We prove that the ring of invariants for triple twists is rationally finitely generated by 13 of these invariants.

Mayer-Rokitansky-Küster-Hauser Syndrome with Rare Findings of Crossed Fused Renal Ectopia and Ovarian Serous Cystadenoma

ABSTRACT The Mayer-Rokitansky-Küster-Hauser (MRKH) syndrome occurs in one of 4,000 to 5,000 female births and is characterized by normal development of secondary sexual, congenital aplasia of uterus and upper part (2/3) of vagina, and normal fallopian tubes and ovaries. Therefore, individuals with MRKH syndrome are at normal risk of developing ovarian neoplasms. We report a case of 19 years old unmarried female who was admitted to the hospital with pain in lower abdomen for 7 months. She was having primary amenorrhea. Gynecological examination revealed a blind vaginal pouch. Rectal examination revealed a large left-sided 8 cm cystic mass which was mobile with a smooth surface. Uterus was not palpable. Phenotypic sex was female. Breast development, axillar and pubic hair development were normal. Abdominopelvic ultrasonography showed left-sided crossed fused renal ectopia and a heterogeneous hypoechoic cystic mass with dense internal echoes on left-side. Uterus was not visualized. Intravenous pyelography also confirmed the finding of left-sided crossed fused renal ectopia. At laparotomy, a 10 × 8 cm cystic hemorrhagic ovarian mass with a single twist of pedicle was found, with a normal right ovary and bilateral tubes. A small hypoplastic unicornuate uterus was present. Cervix was absent. Left-sided Salpingo-oophorectomy was done and tissue was sent for histopathology, which revealed ovarian serous cyst adenoma. All patients with vaginal agenesis must be regarded primarily as a MRKH syndrome and they must be investigated to establish whether there were any associated congenital anomalies. How to cite this article Asnani M, Srivastava K, Inam L, Kunwar S. Mayer-Rokitansky-Küster-Hauser Syndrome with Rare Findings of Crossed Fused Renal Ectopia and Ovarian Serous Cystadenoma. J South Asian Feder Obst Gynae 2015;7(3):220-222.

Networking Seifert surgeries on knots, III

How do Seifert surgeries on hyperbolic knots arise from those on torus knots? We approach this question from a networking viewpoint. The Seifert Surgery Network is a 1-dimensional complex whose vertices correspond to Seifert surgeries; two vertices are connected by an edge if one Seifert surgery is obtained from the other by a single twist along a trivial knot called a seiferter or along an annulus cobounded by seiferters. Successive twists along a "hyperbolic seiferter" or a "hyperbolic annular pair" produce infinitely many Seifert surgeries on hyperbolic knots. In this paper, we investigate Seifert surgeries on torus knots which have hyperbolic seiferters or hyperbolic annular pairs, and obtain results suggesting that such surgeries are restricted.

First Report of Colletotrichum lupini on Lupinus hartwegii and L. mutabilis.

During the 2013 winter cut flower production season, a severe anthracnose epidemic was observed on Lupinus mutabilis (syn L. cruckshanksii) on a commercial flower farm in Martin County, FL. Approximately 50% of the crop was lost to the disease. Symptoms included dark brown, irregularly shaped leaf spots, but more typically, there was a single severe twist in the stem, forming a distinctive necrotic crook. Margins of necrotic lesions were excised and surface sterilized by immersion in 1% sodium hypochlorite for 90 s, rinsed in sterile deionized water, and plated onto potato dextrose agar (PDA). Plates were incubated at approximately 27°C with cycles of 12 h light/12 h darkness. Infected tissue consistently produced colonies that were typical of the genus Colletotrichum. Conidia were primarily oval, with one rounded end and one pointed end, and were highly variable in size, ranging from 10 to 15 μm in length and 3.5 to 5.5 μm in width. Cultures were gray with orange spots, and no setae were observed. These morphological characteristics are consistent with those of Colletotrichum lupini (2). Identification of this species was confirmed by performing a BLASTn search with ITS sequence data (primers ITS4 and ITS5), which shared 99% identity with GenBank submission AJ301968, C. lupini var. setosum strain BBA 71310, isolated from L. luteus in Poland. Inoculum was produced by flooding PDA cultures with sterile deionized water, scraping with a rubber policeman, and passing the suspension through four layers of sterile cheesecloth. This preparation was used to inoculate 10 L. mutabilis and 10 L. hartwegii plants by injecting 10 μl of a suspension of 105 conidia/ml into the stem using a hypodermic needle (1). Ten additional plants were injected with sterile deionized water and maintained with the inoculated plants in the greenhouse for 4 weeks. All of the inoculated plants developed the previously-observed necrotic crook in the stem, whereas control plants developed no symptoms. The same organism was isolated from all inoculated plants. The ITS region was again sequenced, and the Polish strain was the closest match. The Floridian isolate sequence was deposited in GenBank (KF207599). Epidemics of anthracnose on ornamental lupins are common in most areas in which they are grown. In 1939, research plots of L. angustifolius were found with symptoms of anthracnose caused by Glomerella cingulata (3). Although it is not possible to determine if this isolate would be redefined as C. lupini, it does not seem likely since pathogenicity was confirmed on L. angustifolius and L. albus, but it did not cause infection on L. luteus (3) as has been reported for C. lupini (2). The finding of a lupin anthracnose in southeastern Florida is important to both the cut flower producers as well as vegetable producers who might consider some species of Lupinus as potential green manure crops. To the best of our knowledge, this is the first report of C. lupini or any Colletotrichum species on L. hartwegii and L. mutabilis in Florida.

Effect of Twin Delta-Winged Twisted-Tape on Thermal Performance of Heat Exchanger Tube

This work aims at studying the effect of twin delta-winged twisted-tape insertion on heat transfer, pressure drop, and thermal performance characteristics of a heat exchanger tube. All twisted tapes used in this work were made of aluminum sheets twisted at a single twist ratio of 3.0. The twin delta wings were formed by extrusion of the tape at the center area at every twist length interval. For comparison, three different arrangements of the twin delta wings were: (1) the wing tips pointing upstream of the flow (TTW-up, twin delta-winged twisted tape in counterflow arrangement), (2) the wing tips pointing downstream of the flow (TTW-down, twin delta-winged twisted tape in co-flow arrangement), and (3) the wing tips pointing opposite direction (TTW-o, opposite winged twisted tape). The wing declination was arranged at an angle of 15° with respect to the tape surface. Effects of three different wing-tip angles of 20°, 40°, and 60° for a constant wing base were examined. The experiments were conducted using water as the test fluid in a uniform-heat-flux tube for Reynolds number between 5000 and 15,000. The results demonstrate that the TTW-up consistently provides greater heat transfer rate, friction factor, and thermal performance factor than the TTW-down and the TTW-o, at a similar condition. In addition, the heat transfer rate increases as the wing-tip angle decreases. Over the range investigated, the TTW-up with wing-tip angle of 20° gives the highest thermal performance factor of 1.26 along with a Nusselt number and friction factor of 2.57 and 8.55 times those of the plain tube.

Angular dependent reflections of a monodomain blue phase liquid crystal

The angular dependent reflection of a monodomain blue phase liquid crystal (BPLC) is investigated. Unlike a cholesteric liquid crystal with single twist structure, a monodomain BPLC exhibits several reflection orders from different crystal planes. As incident angle increases, the first order reflection experiences a blue shift while the second order experiences a red shift. We analyze the physical mechanism of the reflection from six (110) crystal planes. Good agreement between calculated and experimental results is obtained. Undoubtedly, this angular dependency would affect the performance of BPLC photonic devices that require an oblique incidence.

3,4-Ethylenedioxythiophene in planarizable push–pull oligothiophenes

We report design, synthesis and evaluation of push-pull quaterthiophene amphiphiles containing one 3,4-ethylenedioxythiophene (EDOT) and a single strong twist in the scaffold. Planarizable push-pull oligothiophene amphiphiles have been introduced recently as conceptually innovative fluorescent probes that sense the fluidity and the potential of lipid bilayer membranes. The "hyper-twisted" EDOT probes respond to planarization and restricted rotational freedom with a red shift and changes in vibrational finestructure in the excitation spectrum, respectively. In solution, comparably weak solvatochromism and significant thermochromism are found. Planarization and restricted rotational freedom afford exquisite sensitivity toward nature and fluidity of lipid bilayer membranes, including ratiometric detection of phase transitions. The sensing of membrane potentials is weakened by these unique properties but remains possible.