Zigzag Form Research Articles

An Abstract Concept of Optimal Implementation

In previous works, we introduced Stable Deterministic Residual Structures (SDRSs), Abstract Reduction Systems with an axiomatized residual relation which model orthogonal term and graph rewriting systems, and Deterministic Family Structures (DFSs), which add an axiomatized notion of redex-family to capture known sharing concepts in the λ-calculus and other orthogonal rewrite systems. In this paper, we introduce and study a concept of implementation of DFSs. We show that for any DFS F, its implementation FI is a non-duplicating DFSs with zig-zag as the family relation, where zig-zag is simply the symmetric and transitive closure of the residual relation on redexes with histories. Further, we show that sharing is compositional: the sharing in a DFS F can be decomposed into a weaker sharing F' (such as zig-zag) and a sharing in the implementation F'I of F' stronger than zig-zag. These results require study of the family relation in non-duplicating SDRSs. We show that zig-zag forms a family-relation in every non-duplicating SDRS, and that it is the only separable family relation in such SDRSs.

Pseudosymmetry in tetradecyltrimethylammonium bromide

In the title compound, C17H38N+·Br−, the tetra­decyl chain is extended in a zigzag form. The mol­ecules are packed in layers with the tetra­decyl chains parallel within a layer and antiparallel in alternate layers. There is pseudosymmmetry which emulates a c-halved unit cell in P21/m, but it is not supported by the diffraction pattern, which is consistent with the reported space group and unit cell.

Crystallization Condition of Glassy Syndiotactic Polystyrene in Supercritical CO2

Polymorphism of syndiotactic polystyrene (sPS) induced by supercritical CO2 (scCO2) was investigated as functions of temperature and pressure by using infrared spectroscopy and X-ray diffraction. When a glassy sPS was incubated in scCO2 at 18 MPa, a modification with the trans-trans-gauche-gauche (t2g2) conformation appeared between 40 °C and 80 °C, and the planar zigzag form appeared above 60 °C. Both forms coexisted between 60 °C and 80 °C. Below the critical temperature of CO2 (31.1 °C) no crystallization occurred at any pressure. When the pressure of CO2 is below the critical pressure (7.2 MPa), the t2g2 form did not appear at any temperature but the planar zigzag form appeared above 90 °C. These results indicate that incubation in supercritical CO2 is necessary for the formation of the t2g2 form. On the other hand, the planar zigzag form was obtained irrespective of the physical states of CO2, but depended on the incubation temperature and pressure. This indicates that the conformational stability of the planar zigzag form depends only on the thermal factors. The crystallization temperature into the planar zigzag form decreased with increasing pressure of CO2 due to the plasticizer effect of CO2.

열-기계-전기 하중 하에서의 지능 복합재 평판 고차이론

열-기계-전기 하중이 완전 연계된 스마트 구조물의 응력과 변형을 정확히 예측할 수 있는 판 이론을 개발하였다. 두께 방향으로 변위와 온도장은 3차 곡선에 선형 지그재그 장을 중첩하여 구하였다. 횡 수직방향 변형을 고러하기 위해 횡 수직 변위를 두께방향으로, 포물선으로 가정하였다. 전기장은 선형지그재그 형태로 가정하였다. 스마트 구조물의 층에 의존하는 변위장과 온도장의 자유도를 층 사이의 연속조건과, 평판의 위 아래 횡 방향 전단응력이 존재하지 않는다는 조건으로부터, 기준면에 의한 자유도로 나타내었다. 수치 예를 통해 제안된 이론의 정확도와 효율성을 평가하였다. 본 연구에서 제시한 고차 지그재그 이론은 열 환경 하에서 두꺼운 지능 복합재료 평판의 정적, 동적 거동 해석에 사용될 수 있다. A higher order zig-zag plate theory is developed to accurately predict fully coupled mechanical, thermal, and electric behaviors. Both the in-plane displacement and temperature fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. Smooth parabolic distribution through the thickness is assumed in the transverse deflection in order to consider transverse normal deformation. Linear zig-zag form is adopted in the electric field. The layer-dependent degrees of freedom of displacement and temperature fields are expressed in tern-is of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses and transverse heat flux. The numerical examples of coupled and uncoupled analysis demonstrate the accuracy and efficiency of the present theory. The present theory is suitable for the predictions of fully coupled behaviors of thick smart composite plate under mechanical, thermal, and electric loadings combined.

Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices

AbstractThis paper deals with the formulation of finite plate elements for an accurate description of stress and strain fields in multilayered, thick plates subjected to static loadings in the linear, elastic cases. The so‐called zig‐zag form and interlaminar continuity are addressed in the considered formulations. Two variational statements, the principle of virtual displacements (PVD) and the Reissner mixed variational theorem (RMVT) are employed to derive finite element matrices. Transverse stress assumptions are made in the framework of RMVT and the resulting finite elements describe a priori interlaminar continuous transverse shear and normal stresses. Both modellings which preserve the number of variables independent of the number of layers (equivalent single‐layer models, ESLM) and layer‐wise models (LWM) in which the same variables are independent in each layer, have been treated. The order N of the expansions assumed for both displacement and transverse stress fields in the plate thickness direction z as well as the number of element nodes Nn have been taken as free parameters of the considered formulations. By varying N, Nn, variable treatment (LW or ESL) as well as variational statements (PVD and RMVT), a large number of newly finite elements have been presented. Finite elements that are based on PVD and RMVT have been called classical and advanced, respectively.In order to write the matrices related to the considered plate elements in a concise form and to implement them in a computer code (see Part 2), extensive indicial notations have been set out. As a result, all the finite element matrices have been built from only five arrays that were called fundamental nuclei (four are related to RMVT applications and one to PVD cases). These arrays have 3×3 dimensions and are therefore constituted of only nine terms each. The different formulations are then obtained by expanding the indices that were introduced for the N‐order expansion, for the number of nodes Nn and for the constitutive layers Nl. Compliances and/or stiffness are accumulated from layer to multilayered level according to the corresponding variable treatment (ESLM or LWM). The numerical evaluations and assessment for the presented plate elements have been provided in the companion paper (Part 2), where it has been concluded that it is convenient to refer to RMVT as a variational tool to formulate multilayered plate elements that are able to give a quasi‐three‐dimensional description of stress/strain fields in multilayered thick structures. Copyright © 2002 John Wiley & Sons, Ltd.

Direct trajectory simulation on the growth of carbon nanotubes

Direct trajectory simulations have been carried out to investigate the growth mechanism of single-wall carbon nanotubes from the viewpoint of topological differences in the edge structure, i.e., zigzag or armchair, based on the semiempirical PM3 molecular orbital method. It is shown that the zigzag nanotube can grow smoothly if the zigzag is conserved form, while the armchair nanotube has a tendency to change into the chiral (or zigzag) form. These results agree with the static analysis of frontier electron density distributions in our recent reports as well as with the experimental observations of Sattler et al.

Studies of Chain Conformation in Triblock Oligomers and Microblock Copolymers of Ethylene and Ethylene Oxide

The conformation of ethylene oxide segments has been found to vary when they are incorporated into triblock oligomers [H(CH2)m(CH2CH2O)n(CH2)mH] or microblock copolymers [−(CH2)m(CH2CH2O)n−]x of ethylene (E) and ethylene oxide (EO) depending on the relative length (m vs n) of the sequences. Raman spectroscopy, wide-angle X-ray diffraction, and thermal analysis have been used to investigate these conformational variations. Since both segments crystallize, we have found a profound influence of intermolecular interactions on determining the conformation of the EO segment. In the regime where n 7 (m = 12−20), the EO segments are found to crystallize in the 7/2 helical conformation similar to that found in PEO. In the case where n = 7 (m = 12−20), both the helical and planar zigzag forms of EO are found depending on the thermal and solution proc...

Structural study of the 0.4-nm single-walled carbon nanotubes aligned in channels of AlPO 4-5 crystal

A detailed synthesis process of ultra-small single-walled carbon nanotubes (SWNTs) aligned in the channels of AlPO 4-5 zeolite single crystals is reported. The structure of such ultra-small SWNTs was analyzed by means of transmission electron microscopy (TEM) and polarized Raman scattering. TEM images showed that the diameter of the SWNTs is as small as 0.4 nm, which is the size of three possible structures: the zigzag (5,0), armchair (3,3) and chiral (4,2). The polarization dependence of the Raman lines indicates that the structures of the nanotubes are dominated by the zigzag (5,0) form. Line-shape analysis of the tangential A 1g Raman mode shows that the SWNTs are metallic with a finite electronic density-of-state near the Fermi energy level, which is in agreement with the band structural calculation using local-density function approximation (LDA) as well as the electric transport measurement.

System zones in capillary zone electrophoresis.

This paper brings an overview of system zones (SZs) in capillary zone electrophoresis (CZE) and their effects upon the migration of zones of analytes. It is shown that the formation and migration of SZs is an inherent feature of CZE, and that it depends predominantly on the composition of an actual background electrolyte (BGE). One can distinguish between stationary SZs and migrating SZs. Stationary SZs, which move due to the electroosmotic flow only, are induced in any BGE by sample injection. Migrating SZs may be induced by a sample injection in BGEs which show at least one of the following features: (i) BGE contains two or more co-ions, (ii) BGE has low or high pH whereby H+ or OH- act as the second co-ion, and (iii) BGE contains multivalent weak acids or bases. SZs do not contain any analyte and show always BGE-like composition. They contain components of the BGE only and the concentrations of these components are different from their values in the original BGE. Providing that some of the ionic components of the BGE are visible by the detector, the migrating SZs can be detected and they are present as system peaks/dips in the electropherogram. It is shown that a migrating SZ may be characterized by its mobility, and examples are given how this mobility can depend on the composition of the BGE. Further, the effects of the migrating SZs (either visible or not visible by the detector) upon the zones of analytes are presented and the typical disturbances of the peaks (extra broadening, zig-zag form, schizophrenic behavior) are exemplified and discussed. Finally, some conclusions are presented how to cope with the SZs in practice. The proposed procedure is based on the theoretical predictions and/or measurements of the mobilities of SZs and on the so-called unsafe region. Then, such operational conditions should be selected where the unsafe region is outside of the required analytical window.

Staggered anisotropy parameter modification of the anisotropic t–J model

The anisotropic t-J model ($U_q(gl(2|1))$ Perk-Schultz model) with staggered disposition of the anisotropy parameter along a chain is considered and the corresponding ladder type integrable model is constructed. This is a generalisation to spin-1 case of the staggered $XXZ$ spin-1/2 model considered earlier. The corresponding Hamiltonian is calculated and, since it contains next to nearest neighbour interaction terms, can be written in a zig-zag form. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found.

Infinite chain structures of [Zn(4,4′-bipy)Cl 2] n and [Cu(H 2PO 4)(4,4′-bipy)·2H 2O] n via hydrothermal synthesis

The hydrothermal reactions of zinc chloride with 4,4-bipy and TiO 2, 85% H 3PO 4, CuCO 3·Cu(OH) 2·6H 2O with 4,4′-bipy in water yielded [Zn(4,4′-bipy)Cl 2] n ( I) and [Cu(H 2PO 4)(4,4′-bipy)·2H 2O] n ( II), respectively. Their crystal structures were determined by single-crystal X-ray diffraction analysis. Both compounds possess infinite chain coordination polymeric structures. For I, the chain is in zigzag form with each zinc atom coordinated by two nitrogen atoms from two 4,4′-bipy molecules ligands and two chloride ions in a distorted tetrahedral geometry. For II, the chains are linked by hydrogen bonds to form a three-dimensional network structure and each Cu(I) center is coordinated by two nitrogen atoms from two 4,4′-bipy ligands and one phosphate oxygen atom in a triangular coordination geometry.

Developments, ideas, and evaluations based upon Reissner’s Mixed Variational Theorem in the modeling of multilayered plates and shells

This review article is devoted to the use of the Reissner Mixed Variational Theorem (RMVT) forward two-dimensional modeling of flat and curved, multilayer structures. A thorough review of the literature involving the use in the modeling of multilayered plates and shells using RMVT is also presented. In the first part, the paper overviews relevant key points that should be taken into account for an accurate description of strain and stress fields in multilayered plate and shell analysis. It is then shown that RMVT has been originated in view of the fulfillment of such key points, herein referred to as C0-Requirements (zig-zag form of the displacement fields in the thickness direction and continuity of transverse normal and shear stresses at each layer interface). Classical variational statements are used to introduce Reissner’s Theorem. In the second part, the paper presents various ways in which RMVT can be used to develop plate and shell theories in a systematic manner. The so called layer-wise and equivalent single layer variable description are considered. Both strong and weak (finite element) forms of governing equations have been derived. A Weak Form of Hooke’s Law (WFHL), is also discussed as an idea to eliminate transverse stress variables leading to standard classical models with only displacement unknowns. Two appendices display details of governing equations related to multilayered doubly curved shells and to finite element matrices of multilayered plates. A third part reviews the works that have appeared in literature which make use of RMVT. Mainly papers on multilayered plate and shell modelings have been addressed. The final part of the paper is devoted to giving an overview with selected results of numerical performance that can be acquired by RMVT applications; extensive comparison to elasticity solutions and to other significant analyses, based on classical and refined approaches, are given. It is concluded that Reissner’s Mixed Theorem should be considered as a natural tool for multilayered structure analyses; it plays a similar role to that of the Principle of Virtual Displacement in the analysis of isotropic single-layer structures. This review article includes 119 references.

Investigation of the crystallization process of syndiotactic polypropylene quenched at 0°C from the melt or concentrated solutions by solid-state 13C NMR spectroscopy

The crystallization process of syndiotactic polypropylene (sPP) quenched from the melt or concentrated solutions has been investigated by high-resolution solid-state 13C NMR spectroscopy in order to make clear the formation of the planar zigzag form at 0°C. The sPP film just after quenching at 0°C from the melt is in the noncrystalline state, but when the film is left at room temperature, crystals with sPP in the t 2g 2 conformation are quickly produced. The 13C NMR spectral shape of the CH 2 resonance line is similar to that of the sPP gels previously obtained. For the gels quenched at 0°C from concentrated solutions, T 1C and T 2C measurements reveal that segmental mobility remarkably decreases with increasing polymer concentration in the noncrystalline phase, whereas it stays unchanged in the crystalline phase as a result of lack of penetration of solvent molecules. Increase of viscosity in the noncrystalline phase results in the decrease of molecular mobility. In particular, molecular mobility is extremely restricted in the noncrystalline phase for the solvent-free sample, compared with the case of the gels. A line shape analysis of the CH 3 resonance line indicates that the trans fraction of the noncrystalline component is significantly increased above about 70 wt% concentration. These results lead to the conclusion that the molecular mobility in solutions below about 70 wt% is fast enough to take the almost random chain conformation as expected, but the sPP chains in solutions above about 70 wt% including in the bulk state tend to take trans-rich conformations, probably due to some kind of intermolecular interaction. As a result, crystallization from solutions with appropriate concentrations produces crystals with the most stable t 2g 2 sequences, whereas form III with the planar zigzag conformation is induced around 0°C in the solvent-free bulk state.

Theoretical study of nanotube growth in terms of frontier density distribution

For carbon nanotubes with open end, the relation between the distribution of frontier orbitals and the edge structure was studied by the Hückel and ab initio molecular orbital methods. When the edge of a nanotube takes a zigzag form, the frontier orbitals localize at the edge part irrespective of the tube length, and continuous growth can be expected according to the frontier electron theory; when the edge takes an armchair form, the frontier orbitals delocalize all over the tube surface, disfavoring the nanotube growth. These results coincide with the experimental observation by Sattler et al.

Ropes of BN multi-walled nanotubes

Ropes consisting of tens of multi-walled boron nitride (BN) nanotubes and extending up to several μm were synthesized through a chemical reaction involving chemical-vapor-deposited multi-walled carbon (C) nanotube oxidation by B 2O 3 mixed with either MoO 3 or V 2O 5 in a flowing N 2 atmosphere. The ropes were analyzed by high-resolution transmission electron microscopy (HRTEM) and electron energy loss spectroscopy (EELS). Tubular shells of BN in the ropes were preferentially assembled in a zigzag form with the [10 1 ̄ 0] direction parallel to the tube/rope axis. Oxidation-induced C nanotube opening at the tip and at wall defects, followed by substitution of C atoms with B and N atoms, and consecutive crystallization of BN shells on the seed nanotubes is thought to underlie the formation mechanism.

Crystal Transformation Behavior and Structural Changes of the Planar Zigzag Form for Syndiotactic Polypropylene

Crystal transformation behavior and structural changes for the planar zigzag form (form III) of syndiotactic polypropylene, which is spontaneously crystallized at 0 °C from the melt, have been investigated in the heating process by DSC, wide-angle X-ray diffractometry, and high-resolution solid-state 13C NMR spectroscopy. The DSC curve for the sample containing only form III crystallites, which is crystallized at 0 °C for 5000 h, shows an evident endothermic peak at about 20 °C and an additional exothermic peak at about 100 °C prior to melting at about 150 °C. The endothermic peak, which is shifted up to about 40 °C by annealing at room temperature, is found to be ascribed to the crystal transformation from form III with the planar zigzag conformation to form II composed of isochiral helices with the ttgg conformation by wide-angle X-ray diffractometry. Moreover, the CH3 resonance lines of the dipolar decoupling/MAS 13C NMR spectra measured at different temperatures for the sample with almost the same str...

The first ladder-like lanthanide double chain complex [Tm(NTA)(H 2O) 2]·2H 2O (H 3NTA=nitrilotriacetic acid)

The title complex has been synthesized in aqueous solution and its crystal structure was determined by X-ray diffraction. It consists of a one-dimensional ladder-like chain. One carboxyl group bridges the adjacent Tm ions giving rise to the edge of the ladder, a second one links the Tm ions from the neighboring edge in zigzag form to act as the rung of the ladder, and a third one monodentately coordinates with Tm to serve as the pendant of the ladder. Each Tm ion is eight coordinated by one nitrogen atom, five oxygen atoms from three NTA molecules and two oxygen atoms from H 2O.

Dynamic FT-IR Analysis of the Crystallization to the Planar Zigzag Form for Syndiotactic Polypropylene

The polymorph and crystallization process for syndiotactic polypropylene (sPP) formed around at 0 °C after quenching from the melt has been dynamically investigated by infrared spectroscopy. The observation is carried out at constant temperatures between -5 and 15 °C after quenching into ice-water from the melt. Just after quenching into ice-water from the melt, the specimen is completely in the noncrystalline state with trans-rich sequences. When the samples are kept below 0 °C, only the planar zigzag form (form III) is crystallized in a few hours. Above 5 °C, in addition to the planar zigzag form, form I with the t 2 g 2 conformation is simultaneously formed. Just above the glass transition temperature (around -5 °C), the trans-rich chains are aggregated and developed to form form III. Above 5 °C, the trans-gauche transition is accelerated, and then the helical form with t 2 g 2 conformation is crystallized as form I. The total degree of crystallinity is not so high, because further crystallization is promoted in the noncrystalline region when the sample is left at room temperature after reaching the equilibrium state at each crystallization temperature.

Spontaneous Crystallization Process of the Planar Zigzag Form at 0 °C from the Melt for Syndiotactic Polypropylene

The spontaneous crystallization process of the planar zigzag form (form III) of syndiotactic polypropylene has been investigated at 0 °C for samples quenched from the melt by real-time wide-angle X-ray diffractometry and high-resolution solid-state 13C NMR spectroscopy. The X-ray diffraction profile just after quenched from the melt is in good accord with that of the melt, indicating that the sample is in the noncrystalline state. With increasing crystallization time, broad diffraction peaks assignable to form III are found to evidently appear for the diffraction profile obtained after the subtraction of the noncrystalline contribution. The spontaneous crystallization of form III is also confirmed by high-resolution solid-state 13C NMR spectroscopy; for example, the CH3(I) line assigned to the tt conformation really increased in intensity with increasing crystallization time in concomitancy with the decrease of the CH3(II) line ascribed to the tg conformation. The line shape analysis of these CH3 lines re...

A STUDY OF TRANSVERSE NORMAL STRESS EFFECT ON VIBRATION OF MULTILAYERED PLATES AND SHELLS

This paper evaluates transverse normal stress σzzeffect on vibration of multilayered structures. To this purpose a mixed plate model initially introduced by Toledano and Murakami has been extended to dynamics analysis of double curved shells. These models allow both continuous interlaminar transverse shear and normal stresses as well as the zigzag form of the displacement distribution in the shell thickness directions to be modelled. Governing equations have been derived by employing a Reissner's mixed theorem. Classical models on the basis of standard displacement formulations have been considered for comparison purposes. The evaluations of transverse stress effects have been conducted by comparing constant, linear and higher order distributions of transverse displacement components in the plate thickness directions. Free vibrational response of layered, simply supported plates, cylindrical and spherical shells made of isotropic as well as orthotropic layers has been analyzed. The numerical investigation carried out and comparison with earlier results has concluded that:•1. The possibility of describing interlaminar continuous transverse normal stress makes the mixed theories more attractive with respect to other available modelling.•2. Any refinements of classical models are meaningless, unless the effects of interlaminar continuous transverse shear and normal stresses are both taken into account in a multilayered shell theory.