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.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

The effect of ball milling on the melting behavior of Sn-Cu-Ag eutectic alloy

Sn-Ag-Cu (SAC) solder alloys are the best Pb free alternative for electronic industry. Since their introduction, efforts are made to improve their efficacies by tuning the processing and composition to achieve lower melting point and better wettability. Nanostructured alloys with large boundary content are known to depress the melting points of metals and alloys. In this article we explore this possibility by processing prealloyed SAC alloys close to SAC305 composition (Sn-3wt%Ag-0.5wt%Cu) by mechanical milling which results in the formation of nanostructured alloys. Pulverisette ball mill (P7) and Vibratory ball mills are used to carry out the milling of the powders at room temperature and at lower temperatures (-104 A degrees C), respectively. We report a relatively smaller depression of melting point ranging up to 5 A degrees C with respect to original alloys. The minimum grain sizes achieved and the depression of melting point are similar for both room temperature and low-temperature processed samples. An attempt has been made to rationalize the observations in terms of the basic processes occurring during the milling.

New Look at Kirchhoff's Theory of Plates

KIRCHHOFF’S theory [1] and the first-order shear deformation theory (FSDT) [2] of plates in bending are simple theories and continuously used to obtain design information. Within the classical small deformation theory of elasticity, the problem consists of determining three displacements, u, v, and w, that satisfy three equilibrium equations in the interior of the plate and three specified surface conditions. FSDT is a sixth-order theory with a provision to satisfy three edge conditions and maintains, unlike in Kirchhoff’s theory, independent linear thicknesswise distribution of tangential displacement even if the lateral deflection, w, is zero along a supported edge. However, each of the in-plane distributions of the transverse shear stresses that are of a lower order is expressed as a sum of higher-order displacement terms. Kirchhoff’s assumption of zero transverse shear strains is, however, not a limitation of the theory as a first approximation to the exact 3-D solution.

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Metal chelates in vinyl polymerization: Bulk polymerization of acrylonitrile initiated by Cu(II)-imine complexes

This article deals with the kinetics and mechanism of acrylonitrile (AN) polymerization initiated by Cu(II)-4-anilino 3-pentene 2-one[Cu(II)ANIPO], Cu(II)-4-p-toluedeno 3-pentene 2-one [Cu(II)TPO], and Cu(II)-4-p-nitroanilino 3-pentene 2-one [Cu(II)NAPO] in bulk at 60°C. The polymerization is free radical in nature. The exponent of initiator(I) is 0.5. The initiation step is a complex formation between the chelate and monomer and subsequent decomposition of the intermediate complex giving rise to free radical and Cu(I). This is substantiated by ultraviolet (UV) and electron spin resonance (ESR) studies. The activation energies and kinetic and chain transfer constants have also been evaluated.

Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

On the shear deformation theory for dynamic analysis of beams

Timoshenko's shear deformation theory is widely used for the dynamical analysis of shear-flexible beams. This paper presents a comparative study of the shear deformation theory with a higher order model, of which Timoshenko's shear deformation model is a special case. Results indicate that while Timoshenko's shear deformation theory gives reasonably accurate information regarding the set of bending natural frequencies, there are considerable discrepancies in the information it gives regarding the mode shapes and dynamic response, and so there is a need to consider higher order models for the dynamical analysis of flexure of beams.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Effect of chlorine on the adsorption of oxygen on Cu and Ag surfaces

Based on XPS and UVPS studies, it is shown that oxygen is preferentially adsorbed molecularly in the singlet state on Cu and Ag surfaces containing presorbed chlorine. Adsorption of chlorine on Cu and Ag surfaces containing presorbed atomic oxygen causes a disappearance of the oxygen. Extended Hückel calculations predict the observed behaviour.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Stress-induced martensitic phase transformation in Cu-Zr nanowires

A novel stress-induced martensitic phase transformation in an initial < 100 >/{100} B2-CuZr nanowire is reported for the first time in this letter. Such behavior is observed in a nanowire with cross-sectional dimensions of 19.44 x 19.44 angstrom(2) over a temperature range of 100-400 K and at a strain rate of 1 x 10(9) s(-1) using atomistic simulations. Phase transformation from an initial B2 phase to a BCT (Body-Centered-Tetragonal) phase is observed via nucleation and propagation of {100} twinning plane under high strain rate tensile deformation. (C) 2009 Elsevier B.V. All rights reserved.

Is one-parameter scaling theory of localisation consistent? Comment on Schuh's comment

It is maintained that the one-parameter scaling theory is inconsistent with the physics of Anderson localisation.

A simplified approach to a three-part Wiener-Hopf problem arising in diffraction theory

A direct and simple approach, utilizing Watson's lemma, is presented for obtaining an approximate solution of a three-part Wiener-Hopf problem associated with the problem of diffraction of a plane wave by a soft strip.

Depth profile composition studies of thin film CdS: Cu,S solar cells using XPS and AES

Surface composition and depth profile studies of hemiplated thin film CdS:CuzS solar cells have been carried out using x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) techniques. These studies indicate that the junction is fairly diffused in the as-prepared cell. However, heat treatment of the cell at 210°C in air relatively sharpens the junction and improves the cell performance. Using the Cu(2p3p)/S(2p) ratio as well as the Cu(LVV)/(LMM) Auger intensity ratio, it can be inferred that the nominal valency of copper in the layers above the junction is Cut and it is essentially in the CUSS form. Copper signals are observed from layers deep down in the cell. These seem to appear mostly from the grain boundary region. From the observed concentration of Cd, Cu and S in these deeper layers and the Cu(LVV)/(LMM) ratio it appears that the signals from copper essentially originate partly from copper in CuS and partly from Cu2t trapped in the lattice. It is significant to note that the nominal valence state of copper changes rather abruptly from Cut to Cuz+ across the junction.