The use of synchrotron X-ray scattering coupled with in situ mechanical testing for studying deformation and structural change in isotactic polypropylene

The mechanical behaviour of semi-crystalline polymers is greatly influenced by the properties of the crystalline and the amorphous phases. As a result this topic has been the subject of extensive research. However, to date, a comprehensive relationship between the structure and mechanical properties for semi-crystalline polymers has yet to be established. This present study concerns the commissioning of a novel method for in situ data collection during the deformation of polymers. This involves the combination of three different techniques into a single experiment, namely tensile testing, synchrotron radiation wide angle X-ray scattering, and optical microscopy. For this current investigation, three isotactic polypropylene samples have been studied, produced using different thermal treatments. This enables the influence of thermal treatment on the mechanical properties and crystallographic structure to be assessed. The results indicate that tensile properties are influenced by thermal treatment via the relative fraction of -phase material in the sample. As the temperature increases at which thermal treatment takes place, iPP ductility decreases due to the greater rigidity of the increasing -phase content. Differences in crystal strain between the different iPP crystal phases are also observed although the reasons for such differences remain unclear.     

Polymorphism of hydrogen bonding in the short double helixes of oligonucleotides: Semiempirical quantum chemical study

The origin of heterogeneity of nucleotide steps geometry in short double helixes is studied theoretically. By using the semiempirical MNDO/PM3 technique, the stability of “propeller‐like” and “step‐like” forms of base H‐pairing is examined in the structure of oligonucleotide duplexes of different types. The influence of end effects on the process of nucleotides packing, as well as the dependence of duplex curvature on the nature of bonded oligonucleotides, are examined. It is concluded that the structural polymorphism of base pairs most likely determines the unique packing of complementary pairs and their flexibility in DNA structure. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

On a factorization of the Schrödinger and Klein–Gordon operators

A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order equations to biquaternionic equations of first order. Examples of application of the proposed scheme are presented for both constant and variable coefficients. Copyright © 2008 John Wiley & Sons, Ltd.     

A limit theorem for products of free unitary operators

This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle. The author would like to express his gratitude to Diana Bloom for her help with editing, and to Professor Raghu Varadhan for useful discussions.     

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Light and flexible rotating parts of modern turbine engines operating at supercritical speeds necessitate application of more accurate but rather computationally expensive 3D FE modeling techniques. Stacked disks misalignment due to manufacturing variability in the geometry of individual components constitutes a particularly important aspect to be included in the analysis because of its impact on system dynamics. A new parametric model order reduction algorithm is presented to achieve this goal at affordable computational costs. It is shown that the disks misalignment leads to significant changes in nominal system properties that manifest themselves as additional blocks coupling neighboring spatial harmonics in Fourier space. Consequently, the misalignment effects can no longer be accurately modeled as equivalent forces applied to a nominal unperturbed system. The fact that the mode shapes become heavily distorted by extra harmonic content renders the nominal modal projection-based methods inaccurate and thus numerically ineffective in the context of repeated analysis of multiple misalignment realizations. The significant numerical bottleneck is removed by employing an orthogonal projection onto the subspace spanned by first few Fourier harmonic basis vectors. The projected highly sparse systems are shown to accurately approximate the specific misalignment effects, to be inexpensive to solve using direct sparse methods and easy to parameterize with a small set of measurable eccentricity and tilt angle parameters. Selected numerical examples on an industrial scale model are presented to illustrate the accuracy and efficiency of the algorithm implementation.     

Observation of the chaotic spin-wave soliton trains in magnetic films

The transition from stationary to chaotic spin-wave soliton trains has been observed. The experiment utilized cw excitation of envelope solitons through self-modulation instability of spin waves. By increasing the spin-wave power, the secondary self-modulation instability succeeded the primary modulation instability, resulting in after-modulation of the soliton train amplitude. Further increase of the spin-wave power led to development of the higher-order instabilities, resulting in formation of the chaotic soliton train.     

An example of dynamically induced coherent states

We consider an example where coherent states appear naturally (dynamically). We study the interaction between an arbitrary quantized matter with a quantized electromagnetic field. Using an approximation that is similar to the Hartree–Fock one and a variational principle, we demonstrate that the electromagnetic field is created by the charged matter exactly in Glauber coherent states with parameters determined by mean currents of the matter.     

Slow light on a printed circuit board

Slow-light effects induced by stimulated Raman scattering in polymer waveguides on a printed circuit board are shown to enable a widely tunable delay of broadband optical signals, suggesting an advantageous platform for optical information processing and ultrafast optical waveform transformation.