The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE

It is believed that surface instabilities can occur during the extrusion of linear low density polyethylene due to high extensional stresses at the exit of the die. Local crack development can occur at a critical stress level when melt rupture is reached. This high extensional stress results from the rearrangement of the flow at the boundary transition between the wall exit and the free surface. The stress is highest at the extrudate surface and decreases into the bulk of the material. The location of the region where the critical level is reached can determine the amplitude of the extrudate surface distortion, This paper studies the effect of wall slip on the numerically simulated extensional stress level at the die exit and correlates this to the experimentally determined amplitude of the surface instability. The effect of die exit radius and die wall roughness on extrusion surface instabilities is also correlated to the exit stress level in the same way. Whereas full slip may completely suppress the surface instability, a reduction in the exit stress level and instability amplitude is also shown for a rounded die exit and a slight increase in instability is shown to result from a rough die wall. A surface instability map demonstrates how the shear rate for onset of extrusion surface instabilities can be predicted on the basis of melt strength measurements and simulated stress peaks at the exit of the die. (C) 2001 Elsevier Science B.V. All rights reserved.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Limits to squeezing in the degenerate optical parametric oscillator

We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory.

Crown ether appended cyclam receptors for cationic guests

A series of crown ether appended macrocyclic amines has been prepared comprising benzo-12-crown-4, benzo-15-crown-5, or benzo-18-crown-6 attached to a diamino-substituted cyclam. The Co-III complexes of these three receptors have been prepared and characterized spectroscopically and structurally. Crystal structures of each receptor in complex with an alkali metal ion and structures of the benzo-12-crown-4 and benzo-15-crown-5-receptors without guest ions are reported. 2D NMR and molecular mechanics modeling have been used to examine conformational variations upon guest ion complexation. Addition of cations to these receptors results in an appreciable anodic shift in the Co-III:II 11 redox potential, even in aqueous solution, but little cation selectivity is observed. Evidence for complex formation has been corroborated by Na-23 and Li-7 NMR spectroscopy and electrospray mass spectrometry.

Synthesis and structural properties of patellamide a derivatives and their copper(II) compounds

The synthesis, characterization and copper(II) coordination chemistry of three new cyclic peptide ligands, PatJ(1) (cyclo-(Ile -Thr- (Gly)Thz-lle-Thr(Gly)Thz)), PatJ(2) (cyclo-(Ile-Thr(Gly)Thz-(D)-Ile-Thr-(Gly)Thz)), and PatL (cyclo-(Ile-Ser-(Gly)Thz-Ile-Ser(Gly)Thz)) are reported. All of these cyclic peptides and PatN (cyclo-(Ile-Ser(Gly)Thz-Ile-Thr-(Gly)Thz)) are derivatives of patellamide A and have a [24]azacrown-8 macrocyclic structure. All four synthetic cyclic peptides have two thiazole rings but, in contrast to patellamide A, no oxazoline rings. The molecular structure of PatJ1, determined by X-ray crystallography, has a saddle conformation with two close-to-co-parallel thiazole rings, very similar to the geometry of patellamide D. The two coordination sites of PatJ1 with thiazole-N and amide-N donors are each well preorganized for transition metal ion binding. The coordination of copper(II) was monitored by UV/Vis spectroscopy, and this reveals various (meta)stable mono- and dinuclear copper(II) complexes whose stoichiometry was confirmed by mass spectra. Two types of dinuclear copper(II) complexes, [Cu-2(H4L)(OH2)(n)](2+) (n = 6, 8) and [Cu-2(H4L)(OH2)(n)] (n=4, 6; L=PatN, PatL, PatJ1, PatJ2) have been identified and analyzed structurally by EPR spectroscopy and a combination of spectra simulations and molecular mechanics calculations (MM-EPR). The four structures are similar to each other and have a saddle conformation, that is, derived from the crystal structure of PatJ(1) by a twist of the two thiozole rings. The small but significant structural differences are characterized by the EPR simulations.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states

We show how polarization measurements on the output fields generated by parametric down conversion will reveal a violation of multiparticle Bell inequalities, in the regime of both low- and high-output intensity. In this case, each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behavior possible even where measurements are performed on systems of large quantum (particle) number may be demonstrated. Our proposal applies to both vacuum-state signal and idler inputs, and also to the quantum-injected parametric amplifier as studied by De Martini The effect of detector inefficiencies is included, and weaker Bell-Clauser-Horne inequalities are derived to enable realistic tests of local hidden variables with auxiliary assumptions for the multiparticle situation.

The influence of cis/trans isomerism on the physical properties of a cyano-bridged dinuclear mixed valence complex

The cyano-bridged complexes cis-[L14CoIIINCFeII(CN)5]– and cis-[L14CoIIINCFeIII(CN)5] (L14= 6-methyl-1,4,8,11-tetraazacyclotetradecan-6-amine) are prepared and characterised spectroscopically, electrochemically and structurally: Na{cis-[L14CoIIINCFeII(CN)5]}·9H2O, monoclinic space group P21/c, a= 14.758(3), b= 10.496(1), c= 19.359(3) , = 92.00(2)°, Z= 4; cis-[L14CoIIINCFeIII(CN)5]·4H2O, orthorhombic space group P212121, a= 9.492(1), b= 14.709(2), c= 18.760(3) , Z= 4. In both complexes, the pendant amine is cis to the bridging cyanide ligand. An analysis of the metal-to-metal charge transfer (MMCT) transition in these systems with Hush theory has been carried out. This has revealed that the change in the configuration of the macrocycle both decreases the redox isomer energy difference (E1/2) and increases the reorganisational energy () of the cis-[L14CoIIINCFeII(CN)5]– complex with respect to the trans-[L14CoIIINCFeII(CN)5]– complex, the result being that both isomers display an MMCT transition of similar energy. The variation in redox isomer energy differences of the configurational isomers has been related to strain energy differences by molecular mechanics analysis of the [CoL14Cl]2+/+ precursor complexes.

Squat, stoop, or something in between?

This article reviews the empirical and theoretical bases for recommendations regarding lifting technique. Lifting from postures involving extreme lumbar vertebral flexion, (approximately 60degrees of lumbar flexion, characterised by absence of electromyographical activity in erector spinae) has the potential to contribute to damage to ligaments and intervertebral discs, especially if combined with lateral flexion or rotation. The only appropriate recommendation regarding posture of the lumbar spine during lifting is to avoid postures involving extreme lumbar vertebral flexion (and rotation and lateral flexion). There is no empirical basis for avoiding postures involving moderate lumbar vertebral flexion, and no justification for advocating lifting from a full squat posture. Further, lifting from semi-squat postures, involving a moderate range of flexion at both knees and trunk, allows a pattern of interjoint coordination which appears to be functional in reducing muscular effort. Lifting training is generally ineffective, and there is unlikely to be a single best technique which is appropriate in all situations. Consequently, it may be preferable to provide education in general lifting guidelines and assist lifters to discover individually appropriate postures and patterns of movement. The article concludes by presenting recommendations for lifting technique which are justified by current knowledge.

Control of chaotic instability in a dual-spin spacecraft with dissipation using energy methods

Control of chaotic instability in a rotating multibody system in the form of a dual-spin spacecraft with an axial nutational damper is achieved using an algorithm derived using energy methods. The control method is implemented on two realistic spacecraft parameter configurations which have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude and consequently impair pointing accuracy. The control method is formulated from nutational stability results derived using an energy sink approximation for a dual-spin spacecraft with an asymmetric platform and axisymmetric rotor. The effectiveness of the control method is shown numerically and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and Bifurcation diagrams.

Turbulent flow around a rotating stepped cylinder

Direct numerical simulation (DNS) of turbulent flow around a rotating cylinder with two backward-facing steps axisymmetrically mounted in the circumferential direction was performed and compared with DNS of plane backward-facing step flow (PBSF) of Le [J. Fluid Mech. 330, 349 (1997)]. The original motivation of this work stemmed from the efforts to design a simple device which can generate flows of high turbulence intensity at low cost for corrosion researchers. It turned out that the current flow shows flow structures quite similar to those of PBSF downstream of the step, even though configurations of the two flows are totally different from one another. The stepped cylinder appears to be a cost-effective tool in the generation of flow structures similar to those of PBSF. (C) 2002 American Institute of Physics.

Vibration instability in rolling mills: Modeling and experimental results

Models for the occurrence of the vibrational instability during rolling known as third octave chatter are presented and discussed. An analysis of rolling mill chatter was performed for the purpose of identifying characteristics of the vibrations and to determine any dependency on the rolling schedule. In particular, a stability criterion for the critical rolling speed is used to predict the maximum rolling speed without chatter instability on schedules from a 5 stand tandem mill rolling thin steel product. The results correlate well with measurements of critical speed occurring on the mill using a vibration monitor: This research provides significant insights into the chatter phenomena and has been used to investigate control methods for suppression of the instability.

Simulation of Oxford University Gun Tunnel performance using a quasi-one-dimensional model

The performance of the Oxford University Gun Tunnel has been estimated using a quasi-one-dimensional simulation of the facility gas dynamics. The modelling of the actual facility area variations so as to adequately simulate both shock reflection and flow discharge processes has been considered in some detail. Test gas stagnation pressure and temperature histories are compared with measurements at two different operating conditions - one with nitrogen and the other with carbon dioxide as the test gas. It is demonstrated that both the simulated pressures and temperatures are typically within 3% of the experimental measurements.

Micro-mechanical approximation to the stress field around an inclined fiber of FRCC

Matrix spalling or crushing is one of the important mechanisms of fiber-matrix interaction of fiber reinforced cementitious composites (FRCC). The fiber pullout mechanisms have been extensively studied for an aligned fiber but matrix failure is rarely investigated since it is thought not to be a major affect. However, for an inclined fiber, the matrix failure should not be neglected. Due to the complex process of matrix spalling, experimental investigation and analytical study of this mechanism are rarely found in literature. In this paper, it is assumed that the load transfer is concentrated within the short length of the inclined fiber from the exit point towards anchored end and follows the exponential law. The Mindlin formulation is employed to calculate the 3D stress field. The simulation gives much information about this field. The 3D approximation of the stress state around an inclined fiber helps to qualitatively understand the mechanism of matrix failure. Finally, a spalling criterion is proposed by which matrix spalling occurs only when the stress in a certain volume, rather than the stress at a small point, exceeds the material strength. This implies some local stress redistribution after first yield. The stress redistribution results in more energy input and higher load bearing capacity of the matrix. In accordance with this hypothesis, the evolution of matrix spalling is demonstrated. The accurate prediction of matrix spalling needs the careful determination of the parameters in this model. This is the work of further study. (C) 2002 Elsevier Science Ltd. All rights reserved.