Monolithic carrier-envelope phase-stabilization scheme

A new scheme for stabilizing the carrier-envelope (CE) phase of a few-cycle laser pulse train is demonstrated. Self-phase modulation and difference-frequency generation in a single periodically poled lithium niobate crystal that transmits the main laser beam allows CE phase locking directly in the usable output. The monolithic scheme obviates the need for splitting off a fraction of the laser output for CE phase control, coupling into microstructured fiber, and separation and recombination of spectral components. As a consequence, the output yields 6-fs, 800-nm pulses with an unprecedented degree of short- and long-term reproducibility of the electric field waveform.     

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.     

Methyl methacrylate particles with amino groups on the surface: Colloid stability and sorption of biologically active substances

The present article investigates the influence of dispersion medium on the aggregate stability of cross-linked poly-(methyl methacrylate) particles on the surface layer of which aliphatic amino groups are localized. It is shown that particle size depends on the ionic strength of dispersion medium. The research determines the optimal content of cross-linked agent, ethylene glycol dimetharylate that results in the formation of cationic particles being stable in saline. Particle modification is performed by bovine serum albumin and luminophore fluorescein 5(6)-isothiocyanate. Protein sorption is observed not to influence luminescent properties of the particles. It is also determined that due to the aggregate stability of particles obtained from 5?wt% of ethylene glycol dimethacrylate in saline, the monodispersity and the absence of inversion of zeta potential in wide pH range is retained, such particles may be considered as perspective carriers of biologically active substances.     

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.