Numerical Analysis and Simulation Analysis for Space‐Time Data

Spatio temporal dynamics of the positive column of a dc neon glow discharge is studied and investigated experimentally and theoretically. Spatio temporal analysis by means of biorthogonal decomposition method (BOD) gives insights into the mechanism of irregularity and can be employed for characterization of spatio‐ temporal complexity. In the weak nonlinear region, the wave dynamics is approximated by an amplitude equation of the Ginzburg‐Landau equation (CGLE) with complex coefficients and an additional integral term based on a fluid model. In the present work we deal with irregular spatio‐temporal data. A comparison between the numerical analysis of the experimental data and simulation results are studied. A good agreement between the dynamical behaviour for experimental space‐time data and theoretical simulation space‐time results was obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pd (II)‐catalyzed vinyl addition polymerization of novel functionalized norbornene bearing dimethyl carboxylate groups

Three novel functionalized polynorbornenes (PNB) with pendant dimethyl carboxylate group (carboxylates—acetate, propionate, and butyrate) are synthesized as a vinyl‐type with a palladium (II) catalyst in high yield. The effects of size of substitutents, molar ratio of monomer to catalyst, solvent polarity, reaction time, and temperature on the polymerization of exo‐norbornene dimethyl propionate were systematically investigated. The low molar ratio and temperature, as well as high polarity of solvent, and long reaction time, are favorable for the enhancement of the monomer conversion, especially, the solvent have an obvious effect on the catalyst activity. The resulting poly(cis‐norbornene‐exo‐2,3‐dimethyl carboxylates) (PNB‐dimethyl carboxylates) show good solubility in common organic solvent and high thermal stability up to 360 °C. The glass transition temperature was detected by DMA at 331, 324, and 318 °C for acetate, propionate, and butyrate, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3391–3399, 2007     

On the effect of longitude-dependent fields on convection in stellar atmospheres

In rotating stellar convective zones, heat transfer is shown to be associated with unbalanced azimuth forces arising in the radially ascending (heated) or descending (cold) matter. The presence of a longitude-dependent magnetic field generates additional azimuth forces, hence, new ways of compensating for the unbalanced forces. Generally speaking, this magnetic field is variable but may be nearly static in layers where convective equilibrium is replaced by radiative equilibrium. The condition for the coexistence of the static and usual fields is derived. To this end, an axisymmetric azimuth magnetic field of energy comparable to the energy of rotation should be introduced into models under consideration. In such configurations, conditions for magnetic field generation, as in the Sun, may appear.     

Study of the viscoelastoplastic deformation of an element of a body with a three-branch loading path

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 12, pp. 26–33, December, 1991.     

On the possibility of applying kinoform elements in mirror projectors for EUV lithography

The potential of the technology of reflective diffraction (holographic) optical elements intended for the EUV range is considered, and their application in projection lithography is discussed.     

Mixing characteristics of motionless mixers

Motionless mixers have found a large range of applications, including blending, reaction, dispersion, heat transfer and mass transfer. Understanding the mixing processes that occur in these diverse systems is essential for predicting many aspects of practical importance. The objective of this study is to perform the experimental investigations of mixing characteristics for three different motionless mixers. The red color dye tracer was mixed in the main stream of green hair styling gel, and then the mixing efficiency was quantified by calculating the percentage area concentration of red color at the outlet cross section using a digital image processing technique. In the Sulzer SMX and YHC mixer, a single element mixes the fluid nearly in two dimensions, and three-dimensional mixing is accomplished by the next elements aligned at 90o to their former one. In the Sulzer SMX mixer, the flow appears to be globally well mixed after 5 elements, while in the YHC and YNU mixers, it is necessary to globally well mix more than 1 and 2 elements.     

On a method for studying the norm and the stability of solutions

We present a new method (the method of unitary transformations), which differs from the existing ones, for studying the stability and the norm of solutions of regular and singularly perturbed initial-value problems for nonautonomous linear and quasilinear systems of ODE with normal and “almost normal” matrices. Our results generalize similar theorems for the corresponding systems with constant matrices. This method allows one to avoid rather cumbersome traditional analysis, including the Lyapunov function method. For special classes of singularly perturbed problems, the method provides estimates for the norms of solutions in the presence of exponential or power boundary layers; these observations enrich the collection of known results in this field.     

Lower bounds for positive and negative parts of measures and the arrangement of singularities of their Laplace transforms

For a real measure with variation V(x) satisfying the estimate V(x) ≤ c ₀ exp(Cx) and for the Laplace transform holomorphic in the disk {¦ -C¦ ≤ C} and having at least one pole of order m, we obtain lower bounds for the positive and negative parts of the measure V _± (x) > cx ^m , x > x ₀. We establish lower bounds for V _+- (x) on “short” intervals. Applications to number theory of the results obtained are considered.