Nonlinear acoustic waves in channels with variable cross sections

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted symmetry group is extended and the invariant solutions corresponding to these profiles are obtained. Approximate analytic solutions to the generalized Webster equation are derived for channels with smoothly varying cross sections and arbitrary initial conditions.Comment: Revtex4, 10 pages, 2 figure. This is an enlarged contribution to Acoustical Physics, 2012, v.58, No.3, p.269-276 with modest stylistic corrections introduced mainly in the Introduction and References. Several typos were also correcte

Синтез гідрованих тіофенів реакцією [3+2] циклоприєднання тіокарбоніліліду

Aim. To study the use of chloromethyl trimethylsilylmethyl sulfide as a precursor of thiocarbonyl ylide in [3+2] cycloaddition reaction to a number of α,β-unsaturated compounds and to establish the regularities of the reaction course. To develop an effective method for the synthesis of new dihydro- and tetrahydrothiophene derivatives which are convenient for further modification.Results and discussion. The synthetic approach to tetrahydrothiophenes with substituents in positions 3 and 4 was extended by the [3+2] cycloaddition reaction of thiocarbonyl ylide with a number of compounds containing an activated multiple bond. The stereoselectivity and limitations of this reaction were determined. Further functionalization of the obtained compounds was carried out.Experimental part. Thiocarbonyl ylide was obtained by fluoride ion-promoted 1,3-desilylation of the known chloromethyl trimethylsilylmethyl sulfide. The synthesis of the target compounds involved the [3+2] cycloaddition of such an ylide to a series of compounds with an activated multiple bond. The stereochemistry of the target compounds was determined by 1H NOESY experiments. Synthetic derivatives of thiolancarboxylic acids, in particular aldehydes, alcohols, amines, amidines, were obtained by functionalization of the [3+2] adducts.Conclusions. The synthetic approach to functionalized tetrahydrothiophenes by the [3+2] cycloaddition reaction of thiocarbonyl ylide with a number of compounds containing an activated multiple bond has expanded the limits of application of this reaction and allows obtaining the target compounds in multigram quantities. A high stereoselectivity of this reaction was observed. The reaction products are convenient synthetic precursors to the various classes of organic compounds.Мета. Вивчити використання хлорометилтриметилсилілметил сульфіду як попередника тіокарбоніліліду в реакції [3+2] циклоприєднанні з рядом α,β-ненасичених сполук та виявити закономірності перебігу цієї реакції. Розробити ефективний метод синтезу нових похідних дигідро- та тетрагідротіофенового ряду, які можуть бути зручними для подальшої модифікації.Результати та їх обговорення. Розширено синтетичний підхід до дигідро- та тетрагідротіофенів із замісниками в 3 та 4 положеннях через реакцію [3+2]-циклоприєднання тіокарбоніліліду до ряду сполук з активованим кратним зв’язком. Визначено стереоселективність та межі застосування цієї реакції. Проведено подальшу функціоналізацію отриманих сполук.Експериментальна частина. Тіокарбонілілід було отримано шляхом промотованого флуорид-йоном 1,3-десилілювання відомого хлорометилтриметилсилілметил сульфіду. Синтез цільових сполук передбачав [3+2]-циклоприєднання такого іліду до ряду сполук з активованими кратними зв’язками. Стереохімію цільових сполук визначено за допомогою 1H NOESY експериментів. Функціоналізацією отриманих сполук одержано синтетичні похідні тіоланкарбонових кислот, зокрема альдегіди, спирти, аміни, амідини.Висновки. Синтетичний підхід до функціоналізованих дигідро- та тетрагідротіофенів за допомогою реакції [3+2]-циклоприєднання тіокарбоніліліду з рядом сполук, які містять активований кратний зв’язок, розширив межі застосування цієї реакції і дозволив одержати цільові сполуки у мультиграмових кількостях. Виявлено високу стереоселективність цієї реакції. Продукти реакції є зручними синтетичними попередниками різних класів органічних сполук

Optical models of the molecular atmosphere

The use of optical and laser methods for performing atmospheric investigations has stimulated the development of the optical models of the atmosphere. The principles of constructing the optical models of molecular atmosphere for radiation with different spectral composition (wideband, narrowband, and monochromatic) are considered in the case of linear and nonlinear absorptions. The example of the development of a system which provides for the modeling of the processes of optical-wave energy transfer in the atmosphere is presented. Its physical foundations, structure, programming software, and functioning were considered

Role of direct exchange and Dzyaloshinskii-Moriya interactions in magnetic properties of graphene derivatives: C2_2F and C2_2H

According to the Lieb's theorem the ferromagnetic interaction in graphene-based materials with bipartite lattice is a result of disbalance between the number of sites available for $p_z$ electrons in different sublattices. Here, we report on another mechanism of the ferromagnetism in functionalized graphene that is the direct exchange interaction between spin orbitals. By the example of the single-side semihydrogenated (C$_2$H) and semifluorinated (C$_2$F) graphene we show that such a coupling can partially or even fully compensate antiferromagnetic character of indirect exchange interactions reported earlier [Phys. Rev. B {\bf 88}, 081405(R) (2013)]. As a result, C$_2$H is found to be a two-dimensional material with the isotropic ferromagnetic interaction and negligibly small magnetic anisotropy, which prevents the formation of the long-range magnetic order at finite temperature in accordance with the Mermin-Wagner theorem. This gives a rare example of a system where direct exchange interactions play a crucial role in determining a magnetic structure. In turn, C$_2$F is found to be at the threshold of the antiferromagnetic-ferromagnetic instability, which in combination with the Dzyaloshinskii-Moriya interaction can lead to a skyrmion state.Comment: 10 page