Twist Type Research Articles

Synthesis and stereochemical nonrigidity of isomeric Zn(ii)bis-[N-isopropyloxy(mercapto)naphthaldiminates

Kinetics and reaction mechanisms governing inversion of the tetrahedral configuration at the metal center in the series ofbis-chelate Zn(II) complexes of 3,2-, 1,2-, and 2,1-oxy(mercapto)naphthaldimines, respectively4–6, have been studied with the use of dynamic1H NMR spectroscopy. A polytopal rearrangement of the diagonal twist type has been found to be an energetically preferable pathway of the inversion reaction for complexes4 and5 with a ZnN2O2 coordination site, whereas the inversion reaction for complexes with a ZnN2S2 coordination site occurs by an intramolecular dissociation-recombination pathway that involves cleavage of a Zn-N coordination bond. In the case of complexes6, the inversion reaction is governed mainly by intramolecular degenerate ligand exchange reactions.

Logarithmic correction to the probability of capture for dissipatively perturbed Hamiltonian systems.

Hamiltonian systems are analyzed with a double homoclinic orbit connecting a saddle to itself. Competing centers exist. A small dissipative perturbation causes the stable and unstable manifolds of the saddle point to break apart. The stable manifolds of the saddle point are the boundaries of the basin of attraction for the competing attractors. With small dissipation, the boundaries of the basins of attraction are known to be tightly wound and spiral-like. Small changes in the initial condition can alter the equilibrium to which the solution is attracted. Near the unperturbed homoclinic orbit, the boundary of the basin of attraction consists of a large sequence of nearly homoclinic orbits surrounded by close approaches to the saddle point. The slow passage through an unperturbed homoclinic orbit (separatrix) is determined by the change in the value of the Hamiltonian from one saddle approach to the next. The probability of capture can be asymptotically approximated using this change in the Hamiltonian. The well-known leading-order change of the Hamiltonian from one saddle approach to the next is due to the effect of the perturbation on the homoclinic orbit. A logarithmic correction to this change of the Hamiltonian is shown to be due to the effect of the perturbation on the saddle point itself. It is shown that the probability of capture can be significantly altered from the well-known leading-order probability for Hamiltonian systems with double homoclinic orbits of the twisted type, an example of which is the Hamiltonian system corresponding to primary resonance. Numerical integration of the perturbed Hamiltonian system is used to verify the accuracy of the analytic formulas for the change in the Hamiltonian from one saddle approach to the next. (c) 1995 American Institute of Physics.

On a generic property of geodesic flows

In this paper we are concerned with a sufficient condition for a Riemannian metric on a compact simply–connected manifold to have infinitely many geometrically distinct closed geodesics. 1969 Gromoll–Meyer proved in [GM] that for every Riemannian metric on a compact simply–connected manifold M there are infinitely many geometrically distinct closed geodesics if the sequence (bi(ΛM ;F ))i of Betti numbers of the free loop space ΛM is unbounded for some field F . Using the theory of minimal models Vigue-Poirrier/Sullivan proved that the rational cohomology algebra H∗(M ; I Q) of M is generated by a single element if and only if the sequence (bi(ΛM ; I Q))i of Betti numbers of the free loop space ΛM of M is bounded. It is a conjecture that the same statement holds for all fields of prime characteristic, partial results are due to McCleary–Ziller [MZ] and Halperin/Vigue-Poirrier [HV]. Now we turn to the manifolds for which the hypothesis of Gromoll– Meyer’s theorem does not hold, for example spheres and projective spaces. Then stability properties of the closed geodesics become important. A closed geodesic is hyperbolic if the linearized Poincare map has no eigenvalue of norm 1. From the bumpy metrics theorem due to Abraham [Ab] and Anosov [An2] and from a pertubation result due to Klingenberg–Takens [KT] one can conclude: A C4–generic metric on a compact manifold has either a non–hyperbolic closed geodesic of twist type or all closed geodesics are hyperbolic. In the first case there are infinitely many geometrically distinct closed geodesics in every tubular neighborhood of the closed geodesic of twist type due to a theorem by Moser [Mo]. In the second case there are infinitely many closed geodesics if M is simply–connected due to results by Hingston [Hi] and the author [Ra1]. Hence it follows from these results that a C4–generic metric on a compact simply–connected manifold has infinitely many geometrically distinct closed geodesics. We remark that it is an open question whether there is a Riemannian metric on a simply–connected compact manifold all of whose closed geodesics are hyperbolic. In [Ra2] we show that the examples of metrics on the 2–

Homoclinic twisting bifurcations and cusp horseshoe maps

Chaotic dynamics arises when the unstable manifold of a hyperbolic equilibrium point changes its twist type along a homoclinic orbit as some generic parameter is varied. Such bifurcation points occur naturally in singularly perturbed systems. Some quotient symbolic systems induced from the Bernoulli symbolic system on two symbols are proved to be characteristic for this new mechanism of chaos generation. Combination of geometrical and analytical methods is proved to be more fruitful.

Topological gauged WZW model and two-dimensional gravity

We study the “topological gauged WZW model associated with SU(2)/U(1)”, which is defined as the twisted version of the corresponding supersymmetric gauged WZW model. It is shown that this model is equivalent to a topological conformal field theory characterized by two independent topological conformal algebras, one of which is the “twisted Kazama-Suzuki type” and the other is the “twisted Coulomb gas type”. We further show that our formalism of this gauged WZW model naturally reduces to the well-known formulations of two-dimensional gravity coupled with conformal matter; one of the gauge choices leads to Li's theory, and the alternative choices lead to the KPZ theory or the DDK (Liouville) theory. In the appendix we argue on a possibility of deriving such topological conformal models from the G/G-gauged WZW models.

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.

A TEM study of grain boundaries in zone-melted YBa 2Cu 3O x

Grain boundaries in zone-melted YBa 2Cu 3O x have been studied in detail by means of transmission electron microscopy. Tilt and twist types of low-angle grain boundaries have been observed, which are composed of both edge and screw dislocations. These boundaries possess high crystal coherence and intimate contact. The low-angle boundaries are also found to be free of second phases. Direct dc transport critical current density, J c , at 77 K shows great improvement in the zone-melted sample compared with that of a conventionally sintered sample. The relationship between the enhanced J c and the low-angle grain boundaries is dicussed.

Preparation of Nematic Mixtures from Smectic Compounds

Abstract A simple method has been developed to obtain multicomponent mixtures with a wide range of the nematic phase from smectic compounds. The properties of these mixtures make them suitable for use in displays of twist type.

Structural analysis and superconducting properties of Pb-free Bi 2Sr 2Ca 3Cu 4O y ( n=4, nominal composition)

Bi-based high- T c superconductors of nominal composition Bi 2Sr 2Ca 3Cu 4O 12+ z ( n = 4 phase) were synthesized by an extensive annealing of several hundreds of hours in order to come close to thermodynamic equilibrium. The microstructure reveals an intergrowth of lamellae with different n ( n = 1−5, 7) with an average volume fraction of the n = 4 phase of about 15%. The highest T c is about 110 K and superconducting phases with T c > 110 K are not detectable. However, the distribution of phases with different n is not homogenous but varies considerably between the bulk and the grain boundaries. Especially the n = 2 phase is preferentially located at the grain boundaries and inhibits a continuous superconducting path for the majority n = 3 phase in the ceramic material. In addition to the intergrowth of lamellae with different n special grain boundaries of pure twist and pure tilt type are encountered; the possible role of grain boundaries for flux pinning is discussed.

BOUNDED GENERATION OF CHEVALLEY GROUPS OVER RINGS OF ALGEBRAICS-INTEGERS

Bounded generation is established for elementary subgroups of Chevalley groups of normal and twisted types over rings of algebraic S-integers relative to a set of root elements. Applications of this result to K-theory and the theory of arithmetic groups are given.

Podands Based on 1,4,5,8‐Tetra‐Azaphenanthrene and Their Complexation With Ru2+

AbstractSummary. New podands, based on 1,4,5,8‐tetra‐azaphenanthrene, have been synthesized from 2‐chloro‐1,4,5,8‐tetra‐azaphenanthrene 3; when the anchoring group is a nitrogen atom, the corresponding podands are, however, unstable. When reacted with Ru2+ in an ionizing solvent, podands tris(2‐(2‐(1,4,5,8‐tetra‐azaphenanthryloxy))ethyl)methane 4c and tri(2‐(2‐(1,4,5,8‐tetra‐azaphenanthryloxy))ethyl)trimesoate 9 give only polymeric complexes; in chloroform, complexation stops at bis‐chelation, giving two types of structures. The most intriguing is the twisted type (12, 13) where one of the chelating group has been inverted, giving rise to an unprecedented flattened Ru2+ octahedron.

A 384-kbit/s ISDN burst transceiver

An Integrated Services Digital Network (ISDN) burst transceiver circuit is described which provides two-wire data transmission using the time-compression multiplexing technique and an AMI (alternate mark inversion) line code at a line bit rate of 384 kb/s. An automatic line equalizer handles a wide variety of twisted pair cable types including highly capacitive cables with up to 32-dB insertion loss at the Nyquist frequency.

On torsional loading in an axisymmetric micropolar elastic medium

Effects of torsional loading in an axisymmetric micropolar elastic half-space are studied. The components of microrotation displacement, force stress and couple stress are obtained for a half-space subjected to an arbitrary load produced by shearing stress. A special case of a particular type of twist has been discussed in detail for a specific model and the micropolar effects have been shown graphically.

Non-cancelling infrared divergences in QCD coherent states

The Faddeev-Kulish approach of asymptotic dynamics is used to construct the QCD coherent states at the level of leading and first subleading infrared singularities. Gluon correlations are properly taken into account and an arbitrary number of initial and final partons are considered. The violation of the Bloch-Nordsieck theorem and the cancellation of the Coulomb phase in many-parton initiated processes are conformed. In particular, the non-cancelling terms are given in operator form and are shown to be in general of higher twist type. The physical interpretation and the gauge dependence of the results are also discussed.

1,6-Diamino-2,5-anhydro-1,6-dideoxy- dl-glucitol and some derivatives thereof

1,6-Diamino-2,5-anhydro-1,6-dideoxy- dl-glucitol dihydrochloride and some derivatives were synthesized from 3,5-di- O-acetyl-1,6-dibromo-1,6-dideoxy- d-mannitol. Introduction of the 2,5-anhydro ring and subsequent replacement of the terminal bromine atoms by azide gave low yields of the diazide; therefore, a reverse reaction-sequence was applied. The azido groups were reduced with hydrogen sulfide-pyridine, and the amino groups formed were methylated by using formaldehyde-formic acid and subsequently treating with borohydride. According to 13C-n.m.r. investigations, the symmetrically substituted, 2,5-anhydroglucitol derivatives are present mainly in the 4 T 3 [“north” (N) type of twist] conformation, whereas the analogous l-iditol derivatives mainly adopt the 3 T 4 [“south” (S)] type. The different quaternary salts obtained on methylation of the corresponding 1,6-bis(dimethylamino)derivatives with methyl iodide (aiming at the structure of epi-muscarine) showed no muscarine-like, biological activity.

Net subgroups of Chevalley groups

We introduce and study net subgroups of Chevalley groups of normal and certain twisted types. Another subgroup of Chevalley groups related to a net was discussed in Ref. Zh. Mat. 1976; 10A151; 1977, 10A301; 1978, 6A476.

Parabolic subgroups of twisted Chevalley groups over a semilocal ring

It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group G ρ (Φ, R) of twisted type Φ=Al,l odd, Dl, E6 over a commutative semilocal ring R with involution ρ are in one-to-one correspondence with the ρ-invariant parabolic nets of ideals of R of type Φ, i.e., with the sets , of ideals σ α of R such that: (l) whenever ; (2)ρσ α =σ ρα for all α; (3) σ α =R forα > 0. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.

Topotactic lithium reactions with ReO3 related shear structures

Several examples of compounds with the ReO3 structure and shear structures derived from it have been lithiated using n-BuLi. Lithiation of ReO3 results in two new hexagonal compositions LiReO3 and Li2ReO3 which are related to cubic ReO3 by a simple twist of the structure. The extensively edge shared structured of FeV3O8 forms Li2FeV3O8 which contains a similar amount of lithium on a per cavity basis, but cannot undergo this type of twist. Results on similar compounds are also discussed.

An Infinite Class of Deltahedra

The appropriate designation deltahedra (A-hedra) has been proposed by Cundy [1] for polyhedra all faces of which are equilateral triangles. Three of the regular (Platonic) solids the tetrahedron, octahedron, and icosahedron are convex deltahedra with 4, 8, and 20 equilateral triangular faces, respectively. Models of deltahedra can be made conveniently by using No. 10 rubber bands to join the 3-inch flanged equilateral triangle cardboard invented by Seattle architect, Fred Bassetti [2]. Kits of these Poly-O panels can be purchased from Book-Lab, Inc. [3]. Or, home-made can be cut from railroad board in the manner clearly described by Stewart [4], Pritchett [5], and Woolaver [6]. Three convex deltahedra can be formed by placing together the bases of two congruent pyramids: the 6-faced triangular dipyramid or ditetrahedron, the 8-faced square dipyramid or octahedron, and the 10-faced pentagonal dipyramid. Six equilateral triangles can be assembled into a regular hexagon. Two such hexagons joined around their perimeters form a degenerate dipyramid. If this is separated into two parts along two coincident long diagonals, the two parts can be opened up by pressing inward on the ends of the diagonals. After one of the opened parts is rotated through 900, the two parts can be rejoined to form a 12-faced Siamese dodecahedron which is convex. There are only eight convex deltahedra [7]. Completing the set are the 14-faced triaugmented triangular prism, formed by attaching square pyramids to the square lateral faces of a triangular prism; and the 16-faced dicapped square antiprism, formed by attaching square pyramids to the two bases of a square antiprism. Thus the eight convex deltahedra are formed from 4, 6, 8, 10, 12, 14, 16 and 20 equilateral triangles. There are no convex deltahedra with 18 faces, nor any with more than 20 faces. Once convexity is abandoned, the possibilities of forming deltahedra are endless. Members of one particularly interesting and attractive type are made by attaching regular tetrahedra to some or all of the faces of other deltahedra. The deltahedra thus made by augmentation are pseudo-stellated, since they are not the same as the solids produced by extending the planes of the faces of the basic polyhedron, except in the case of the augmented octahedron which is Kepler's famous stella octangula. A particularly attractive model is the pseudo-stellated icosahedron. Models of an infinite subclass of deltahedra, the spiral (twisted) type, can be constructed from strips of equilateral triangles (FIGURE 1) flexing about the common sides. Any desired lengths of these strips can be formed easily by the cardboard panel-rubber band method. Models of spiral deltahedra can be started by joining the sides of the left-most angles of three strips to form a trihedral angle. The construction proceeds by joining sides of triangles of adjacent strips that have an end in common. (Differently colored strips emphasize the spiral nature of the deltahedron.) The three strips may be chosen from the Hand L-patterns in four ways, namely: HHH, LLL, HHL, and LLH. The HHH form appears to twist to the right (see FIGURE 2), and the LLL form appears to twist to the left. However, in general, each form consists of a pile of regular octahedra capped top and bottom with a

Dislocation substructure of mantle-derived olivine as revealed by selective chemical etching and transmission electron microscopy

Cleaved and mechanically polished surfaces of olivine from peridotite xenoliths from San Carlos, Arizona, were chemically etched using the techniques of Wegner and Christie (1974). Dislocation etch pits are produced on all surface orientations and they tend to be preferentially aligned along the traces of subgrain boundaries, which are approximately parallel to (100), (010), and (001). Shallow channels were also produced on (010) surfaces and represent dislocations near the surface that are etched out along their lengths. The dislocation etch channel loops are often concentric, and emanate from (100) subgrain boundaries, which suggests that dislocation sources are in the boundaries. Data on subgrain misorientation and dislocation line orientation and arguments based on subgrain boundary energy minimization are used to characterize the dislocation structures of the subgrain boundaries. (010) subgrain boundaries are of the twist type, composed of networks of [100] and [001] screw dislocations. Both (100) and (001) subgrain boundaries are tilt walls composed of arrays of edge dislocation with Burgers vectors b=[100] and [001], respectively. The inferred slip systems are {001} 〈100〉, {100} 〈001〉, and {010} 〈100〉 in order of diminishing importance. Exploratory transmission electron microscopy is in accord with these identifications. The flow stresses associated with the development of the subgrain structure are estimated from the densities of free dislocations and from the subgrain dimensions. Inferred stresses range from 35 to 75 bars using the free dislocation densities and 20 to 100 bars using the subgrain sizes.