An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

Screw dynamo and the generation of nonaxisymmetric magnetic fields

A mechanism is presented here for the amplification of large-scale nonaxisymmetric magnetic fields as a manifestation of the dynamo effect. We generalize a result on restrictions of dynamo actions due to laminar flow originally derived by Zeldovich, Ruzmaikin, and Sokolov [Magnetic Fields in Astrophysics (Gordon and Breach, New York, 1983)]. We show how a screwlike motion having phi and z components of velocity can help to grow a magnetic field. This model postulates a large-scale flow having phi and z components with radial dependences (helical flow). Shear in the radial field, because of a near-flux-freezing condition, causes amplification of the phi component of the magnetic field. The radial and axial components grow due to the presence of turbulent diffusion. The shear in the large scale flow induces an indefinite growth of magnetic field without the a effect; nevertheless, turbulent diffusion forms an important part in the overall mechanism.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Application of a modified jogged-screw model for creep of titanium aluminides: evaluation of the key substructural parameters

A modification of the jogged-screw model has been adopted recently by the authors to explain observations of 1/2[110]-type jogged-screw dislocations in equiaxed Ti-48Al under creep conditions. The aim of this study has been to verify and validate the parameters and functional dependencies that have been assumed in this previous work. The original solution has been reformulated to take into account the finite length of the moving jog. This is a better approximation of the tall jog. The substructural model parameters have been further investigated in light of the Finite Length Moving Line (FLML) source approximation. The original model assumes that the critical jog height (beyond which the jog is not dragged) is inversely proportional to the applied stress. By accounting for the fact that there are three competing mechanisms (jog dragging, dipole dragging, dipole bypass) possible, we can arrive at a modified critical jog height. The critical jog height was found to be more strongly stress dependent than assumed previously. The original model assumes the jog spacing to be invariant over the stress range. However, dynamic simulation using a line tension model has shown that the jog spacing is inversely proportional to the applied stress. This has also been confirmed by TEM measurements of jog spacings over a range of stresses. Taylor's expression assumed previously to provide the dependence of dislocation density on the applied stress, has now been confirmed by actual dislocation density measurements. Combining all of these parameters and dependencies, derived both from experiment and theory, leads to an excellent prediction of creep rates and stress exponents. The further application of this model to other materials, and the important role of atomistic and dislocation dynamics simulations in its continued development is also discussed.

Structure of 5-Bromo-2',3'-O-isopropylideneuridine, C12H15BrN206

Mr= 363.17, orthorhombic, P21212 ~, a= 5.251(4), b=14.962(5), c=19.112(5)A, U= 1501.41/k 3, Z=4, Dx=1.61Mgm -3, /t(CuKa)= 3.02 mm -1, 2(Cu Ka)= 1.5418/~, final R = 7.0% for 1091 reflections with Fo> 2e(Fo). The glycosidic torsion angle ZCN is 13"1 (12) °. The ribose has a C (3')-exo,C (4)-endo twist geometry. The dioxolane ring assumes an envelope conformation with 0(3') displaced by 0.453 (10)/k from the plane of the other four atoms. The conformation about the C(4')-C(5') bond is gauche-gauche. The structure is stabilized by two hydrogen bonds between screw-axis-related molecules. The crystal packing and the conformation of the molecule are very similar to those found in the structure of 2',3'-O-isopropylideneuridine which lacks the Br atom at the 5-position.

Structure of 2',3'-O-Isopropylidene-5'-O-tosyluridine, C19H22N 2Oas

M r = 438.45, trigonal, P32, a = b = 13.385 (4), c = 9.900 (5) A,, V = 1536.0 A 3, Z = 3, D x = 1.42, D m = 1.42 Mg m -3, 2(Cu Ka) = 1.5418 A,,g(CuKa) = .800mm -], T=290K, F(000)=690, R=6.0% for 1222 unique reflections with F o>_2o(Fo). This is the first 2',3'-O-isopropylidene pyrimidine nucleoside with the base in a syn orientation with respect to the ribose [Xcy= 116.0(7)°]. The ribose has a C(3')-endo conformation with the phase angle of pseudorotation P = 16.36 (2) °. The dioxolane ring assumes an envelope conformation with 0(2') displaced from the best four-atom plane by 0.50 (1) k. The crystal structure is possibly stabilized by a bifurcated hydrogen bond between N(3) and the 0(2) and 0(4) atoms of screw-related molecules.

N-Acetylglycyl-L-lysine methyl ester acetate

C llH22 N 30 + . C2H302, orthorhombic, P2~2~2~, a = 5.511(2), b = 14.588(4), c = 21.109 (4)A, Z = 4. The structure has been solved using MULTAN and refined to R = 0.079 for 993 observed reflections. The fully extended lysine side chain in the molecule is staggered between the main-chain amino and carbonyl groups. The dipeptide molecules in the crystal structure are arranged in twofold helices centred on 21 screw axes. These helices are interconnected through interactions involving the acetate and the side-chain amino groups. Each acetate group bridges two adjacent side-chain amino groups, related by an a translation, giving rise to an infinitely long chain of alternating negatively charged carboxylate and positively charged amino groups.

N-Acetylglycyl-L-lysine methyl ester acetate

C llH22 N 30 + . C2H302, orthorhombic, P2~2~2~, a = 5.511(2), b = 14.588(4), c = 21.109 (4)A, Z = 4. The structure has been solved using MULTAN and refined to R = 0.079 for 993 observed reflections. The fully extended lysine side chain in the molecule is staggered between the main-chain amino and carbonyl groups. The dipeptide molecules in the crystal structure are arranged in twofold helices centred on 21 screw axes. These helices are interconnected through interactions involving the acetate and the side-chain amino groups. Each acetate group bridges two adjacent side-chain amino groups, related by an a translation, giving rise to an infinitely long chain of alternating negatively charged carboxylate and positively charged amino groups.

Tris(tert-butyl 3-oxobutanoato-kappa O-2(1),O- )-aluminium(III) at 153 K

In the title complex, [Al(C8H13O3)(3)], a potential metal-organic chemical vapour deposition (MOCVD) precursor, three bidentate ligand molecules are bound to the metal atom, forming an octahedral geometry. Two non-planar six-membered chelate rings adopt screw-boat conformations, while the third ring has a conformation that lies about halfway between an envelope and a screw-boat.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

Anomalin. A Dihydropyranocoumarin Derivative from the Plant Lingusticum elatum

The title compound, 9,10-dihydro-8,8-dimethyl-2-oxo-2H,8H-benzo[1,2-b:3,4-b']dipyran-9,10-diyl 2-methyl-2-butenoate, C24H26O7, contains a highly planar coumarin nucleus and a substituted dihydropyran ring (C), which has a distorted half-chair conformation, with an 8 alpha,9 beta orientation. The conformation of ring C is further supported by the two angelyloxy (2-methyl-2-butenoyloxy) substituents at positions C9 and C10, which are cis oriented and thus cannot both occupy equatorial positions with respect to the plane of ring C. The conformations of the two angelyloxy substituents are different, as indicated by their endocyclic torsion angles. The most striking of these angles are O1'-C2'-C4'=C6' and O1'-C2'-C4'-C5' [-137.7 (5) and 43.7 (5)degrees, respectively, in the chain at C10 and 155.8 (5) and -24.7 (9)degrees, respectively in the chain at C9]. These variations are due to two intramolecular hydrogen bonds, namely, C16-H161 ... O1' [C16 ... O1' 3.056 (7) Angstrom] and C7''-H7Y ... O3'' [C7'' ... O3'' 2.955 (12) Angstrom]. The methyl substituents, C15 and C16, at position C8 are alpha and beta oriented, respectively. The crystal structure is stabilized by a weak C4-H41 ... O3' hydrogen bond [C4 ... O3' 3.297 (6) Angstrom] between the screw-related molecules.

Dynamic recrystallisation during hot working of Zr-2 center dot 5Nb: Characterisation using processing maps

The characteristics of the hot deformation of Zr-2.5Nb (wt-%) in the temperature range 650-950 degrees C and in the strain rate range 0.001-100 s(-1) have been studied using hot compression testing. Two different preform microstructures: equiaxed (alpha + beta) and beta transformed have been investigated. For this study, the approach of processing maps has been adopted and their interpretation carried out using the dynamic materials model. The efficiency of power dissipation given by [2m/(m + 1)], where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of dynamic recrystallisation has been identified in the maps of equiaxed (alpha + beta) and beta transformed preforms. In the case of equiaxed (alpha + beta), the stress-strain curves are steady state and the dynamic recrystallisation domain in the map occurs with a peak efficiency of 45% at 850 degrees C and 0.001 s(-1). On the other hand the beta transformed preform exhibits stress-strain curves with continuous flow softening. The corresponding processing map shows a domain of dynamic recrystallisation occurring by the shearing of alpha platelets followed by globularisation with a peak efficiency of 54% at 750 degrees C and 0.001 s(-1). The characteristics of dynamic recrystallisation are analysed on the basis of a simple model which considers the rates of nucleation and growth of recrystallised gains. Calculations show that these two rates are nearly equal and that the nucleation of dynamic recrystallisation is essentially controlled by mechanical recovery involving the cross-slip of screw dislocations. Analysis of flow instabilities using a continuum criterion revealed that Zi-2.5Nb exhibits flow localisation at temperatures lower than 700 degrees C and strain rates higher than 1 s(-1).

Dehydrophenylalanine zippers: strong helix-helix clamping through a network of weak interactions

A decapeptide Boc-L-Ala-(DeltaPhe)(4)-L-Ala-(DeltaPhe)(3)-Gly-OMe (Peptide I) was synthesized to study the preferred screw sense of consecutive alpha,beta-dehydrophenylalanine (DeltaPhe) residues. Crystallographic and CD studies suggest that, despite the presence of two L-Ala residues in the sequence, the decapeptide does not have a preferred screw sense. The peptide crystallizes with two conformers per asymmetric unit, one of them a slightly distorted right-handed 3(10)-helix (X) and the other a left-handed 3(10)-helix (Y) with X and Y being antiparallel to each other. An unanticipated and interesting observation is that in the solid state, the two shape-complement molecules self-assemble and interact with an extensive network of C-H...O hydrogen bonds and pi-pi interactions, directed laterally to the helix axis with amazing regularity. Here, we present an atomic resolution picture of the weak interaction mediated mutual recognition of two secondary structural elements and its possible implication in understanding the specific folding of the hydrophobic core of globular proteins and exploitation in future work on de novo design.

Helical structures: The geometry of protein helices and nanotubes

In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A helical structure is thus generated by the repeated action of a screw transformation acting on a subunit. A plane hexagonal lattice wrapped round a cylinder provides a useful starting point for describing the helical conformations of protein molecules, for investigating the geometrical properties of carbon nanotubes, and for certain types of dense packings of equal spheres.