Kinetics of two-step nucleation of crystals

When the nucleation of a stable crystalline phase directly in a supersaturated old phase is greatly retarded, the crystal nuclei might nucleate within faster-forming particles of an intermediate phase. Here we present a theoretical investigation of the kinetics of this two-step nucleation of crystals and derive general expressions for the time dependence of the number of crystals nucleated within the particles of the intermediate phase. The results reveal that crystal nucleation can be strongly delayed by the slow growth of the particles and/or by the slow nucleation of the crystals in them. Furthermore, the linear part of the time dependence of the number of nucleated crystals is determined by the formation rate of the intermediate particles. This is in contrast with the one-step nucleation of crystals when this linear part is determined by the rate of crystal nucleation directly in the old phase. Criteria are proposed for distinction between the one- and two-step nucleation mechanisms, based on the supersaturation dependence of the delay time for nucleation. The application of the theoretical approach to the analysis of experimental data on the nucleation of crystals and other ordered aggregates of protein and other soluble materials is discussed.     

Polymerization dynamics of double-stranded biopolymers: chemical kinetic approach

The polymerization dynamics of double-stranded polymers, such as actin filaments, is investigated theoretically using simple chemical kinetic models that explicitly take into account some microscopic details of the polymer structure and the lateral interactions between the protofilaments. By considering all possible molecular configurations, the exact analytical expressions for the growth velocity and dispersion for two-stranded polymers are obtained in the case of the growing at only one end, and for the growth from both polymer ends. Exact theoretical calculations are compared with the predictions of approximate multilayer models that consider only a finite number of the most relevant polymer configurations. Our theoretical approach is applied to analyze the experimental data on the growth and fluctuations dynamics of individual single actin filaments.     

The interactive fixed charge inhomogeneous flows optimization problem

An optimization problem of interactive inhomogenous flows (Steiner multicommodity network flow problem) is formulated. The problem's main characteristic is a fixed charge change when combining multicommodity communications. In this paper we propose a method for solving this problem which, in order to restrict the search on the feasible domain, reduces the original problem to a concave programming problem in the form: min {f(x)|xX} wheref:ⁿ is a concave function, andX ₀ ⁿ is a flow polytope defined by network transportation constraints. For practical large-scale problems arising from planning transportation networks on inhomogeneous surfaces defined by a digital model, a method of local optimization over a flow polytope vertex set is proposed, which is far more effective in comparison with the Gallo and Sodini method under polytope strong degeneracy conditions.     

Generalizations of the odd degree theorem and applications

LetV ⊂ ℙℝ ⁿ be an algebraic variety, such that its complexificationV _ℂ ⊂ ℙ ⁿ is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ ⁿ of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3.     

Reconstruction of the fine structure of an acoustic scatterer against the distorting influence of its large-scale inhomogeneities

In the ultrasonic diagnostics of small-size neoplasms of biological tissues at the earliest stage of their development, an efficient way to eliminate the distorting influence of high-contrast or large inhomogeneities of the biological medium is to apply the iterative technique. A simple approach is proposed, which makes it possible with only two iteration steps to achieve an efficient focusing of the tomograph array. At the first step, the unknown distribution of the large-scale inhomogeneities of sound velocity and absorption over the scatterer is reconstructed, where the large-scale inhomogeneities are those whose size exceeds several wavelengths. At the second step, the fine structure of the scatterer is reconstructed against the large-scale background, which can be performed with a high accuracy owing to the evaluation of the background at the first step. The possibility of simultaneous reconstruction of the large-scale and fine structures by the noniterative Grinevich-Novikov algorithm is considered as an alternative. This algorithm reconstructs in an explicit form two-dimensional refractive-absorbing acoustic scatterers of almost arbitrary shape and strength. Taking into account the effects of multiple scattering, this algorithm provides resolution of the fine structure almost as good as that achieved in reconstructing the same structure against an undistorting homogeneous background. The results of numerical simulations of both algorithms are presented.     

Observations of surface modifications induced by the multiple pulse irradiation using a soft picosecond x-ray laser beam

To study the interactions between picosecond soft x-ray laser (SXRL) beams and material surfaces, gold (Au), copper (Cu), and silicon (Si) surfaces were irradiated with SXRL pulses having a wavelength of 13.9 nm and a duration of ～7 ps. Following irradiation, the surfaces of the substrates were observed using a scanning electron microscope and an atomic force microscope. With single pulse irradiation, ripple-like structures were formed on the Au and Cu surfaces. These structures were different from previously investigated conical structures formed on an Al surface. In addition, it was confirmed that the development of modified structures, i.e., growth of hillocks on the Au and Cu surfaces, was observed after multiple SXRL pulse exposures. However, on the Si surface, deep holes that seemed to be melted structures induced by the accumulation of multiple pulses of irradiations were found. Therefore, it was concluded that SXRL beam irradiation of various material surfaces causes different types of surface modifications, and the changes in the surface behaviors are attributed to the differences in the elemental properties, such as the attenuation length of x-ray photons.     

One-pot five-component high diastereoselective synthesis of polysubstituted 2-piperidinones from aromatic aldehydes,nitriles, dialkyl malonates and ammonium acetate

Molecular Diversity - A novel five-component diastereoselective synthesis of polysubstituted 2-piperidinones is reported. The Knoevenagel condensation–Michael addition–Mannich cascade...     

Phase-sensitive scattering of a continuous wave on a soliton

Using cross-correlation frequency-resolved optical gating, we observe the phase-sensitive resonance in the interaction of a soliton with a continuous wave in a photonic crystal fiber. This interaction strongly depends on the difference in the phase velocities of the orthogonally polarized fiber modes and leads to generation of a new spectral peak. The spectral and temporal structure of this signal is revealed in our measurements, which are supported by analytical theory and numerical simulations.     

Demonstration of fiber-laser-produced plasma source and application to efficient extreme UV light generation

Efficient generation of extreme UV (EUV) light at lambda = 13.5 nm from a bulk Sn target has been demonstrated by using a fiber laser. The conversion efficiency from the 1064 nm IR to the EUV was measured to be around 0.9% into 2pi steradians within a 2% bandwidth. To the best of our knowledge, this is the first time an all-fiber system was used to generate EUV or soft x rays.     

Effects of metal and “magnetic wall” on the dispersion characteristic of magnetostatic waves

The dispersion relation of magnetostatic waves tangentially magnetized to saturation ferrite film, with a “magnetic wall” condition (tangential component of microwave magnetic field is equal to zero) on one of the film surface and with a metal condition on the opposite surface is analyzed. The dispersion characteristics show that unidirectional magnetostatic waves appear in this structure: they can transfer energy in one direction only and fundamentally cannot transfer energy in the opposite direction. The dispersion-free propagation of magnetostatic waves also is possible in the structure in a wide frequency interval.