Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

中长跑的选材与预测

本文从系统学角度,探讨如何控制中长跑选材的过程,并从生理、心理、身体素质以及身体形态等方面探讨如何以科学的选材方法和手段为依据,指导教练选出优秀人材,进行早期培养,缩短其成材周期,提高成材率。     

Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

The results from an experimental study into the dynamic behavior of a gas-liquid medium and solid particles in a compound shell (sphere-truncated cone) are reported on. The following processes are studied: formation of gas bubbles and their clusters, strong macroflows, and intensive chaotic motion of the medium in the truncated cone as a nonlinear vibrating liquid-gas system__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 112–118, January 2005.     

Quantum-Chemical Evaluation of the Protolytic Properties of Thiophenols

The enthalpies and free energies of proton affinity (PA) were calculated by the PM3 method for 27 thiophenoxide anions. For thiophenols, linear correlation has been found between the PAs and the values of pK _a measured by different authors in aqueous acetone, aqueous ethanol, and methanol media. The dependences found permit one to predict a priori the protolytic properties of thiophenols. The differential effects of aqueous ethanol media with different ethanol contents on thiophenol acidity were evaluated based on quantum-chemical data.Original Russian Text Copyright © 2004 by A. N. Pankratov and A. V. Shalabai__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 800–806, September–October, 2004.     

Stress and heat flux stabilization for viscous compressible medium equations with a nonmonotone state function

We study a system of quasilinear equations describing one-dimensional flow of a viscous compressible heat-conducting medium with a nonmonotone state function and mass force. The large-time behavior of solutions is considered for arbitrarily large initial data. In spite of possible nonuniqueness and discontinuity of the stationary solution, we prove L²-stabilization for the stress and heat flux as t → ∞ along with corresponding global energy estimates for them. The new method of proof utilizes a combination of energy type equalities for the stress and heat flux. Consequently, H¹-stabilization of the velocity and temperature along with global estimates for their derivatives are valid as well.     

视觉与材质——油画颜料的视觉效果

本文通过对佛兰德斯和北欧、意人利和南欧的色层语言的分析,可以看出油画这种艺术形式之所以能长时期吸引人们,与它的材质密切相关。这种由材质形成的色层语言不仅生动地表现了对自然的摹仿,而且体现出它独特的色层美感。     

Radiation Transfer in a Binary, Stochastic Medium with Strongly Fluctuating Parameters

The propagation of radiation in a three-dimensional, inhomogeneous, stochastic, scattering medium and in an equivalent homogeneous medium has been investigated by the small-angle iteration method. The statistical structure of the scattering parameters of a three-dimensional medium has been described within the framework of the two-dimensional Poisson process and the binary Markov process. The analytical data obtained point to the fact that the three-dimensional inhomogeneity of a stochastic medium significantly influences the radiation transfer in it.     

Green chemical synthesis of fluorinated 1,3,5-triaryl-s-triazines in aqueous medium under microwaves as potential antifungal agents

Reasonable pure fluorinated s-triazines were synthesized in quantitative yield (96-99%) in 2-3 min in aqueous medium under microwaves, by reaction of fluorinated anilines and aqueous formaldehyde. All synthesized compounds have been screened in vitro for their antifungal activity against Rhizoctonia solani, Fusarium oxysporum, and Collectotrichum capsici.     

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.