The Muskat problem at the microscopic level for a single capillary

We consider the evolution of the free boundary separating two immiscible viscous fluids with different constant densities. The motion is described by the Stokes equations driven by the input pressure and gravity force. For flows in a bounded domain Ω⊂R², we prove existence and uniqueness of classical solutions and make an emphasis on the study of properties of the moving boundary separating the two fluidsyesBelgorod State National Research Universit

Avoidability of formulas with two variables

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We consider the patterns such that at most two variables appear at least twice, or equivalently, the formulas with at most two variables. For each such formula, we determine whether it is $2$-avoidable, and if it is $2$-avoidable, we determine whether it is avoided by exponentially many binary words

Single-shot carrier-envelope-phase measurement in ambient air

The ability to measure and control the carrier envelope phase (CEP) of few-cycle laser pulses is of paramount importance for both frequency metrology and attosecond science. Here, we present a phase meter relying on the CEP-dependent photocurrents induced by circularly polarized few-cycle pulses focused between electrodes in ambient air. The new device facilitates compact single-shot, CEP measurements under ambient conditions and promises CEP tagging at repetition rates orders of magnitude higher than most conventional CEP detection schemes as well as straightforward implementation at longer wavelengths

Multiscale theory of turbulence in wavelet representation

We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of its wavelet components, we achieve the cancellation of loop divergences in the stochastic perturbation expansion. An extra contribution to the energy transfer from large to smaller scales is considered. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures based on the wavelet decomposition are constructed.Comment: LaTeX, 27 pages, 3 eps figure

Regional per capita income differences: Spatial and hierarchical dependencies

Relevance. Regional differences in per capita income are a matter of concern for many countries for many reasons, including the threat that such regional disparities pose to national security. Multiple tools and methods are used to investigate these disparities and fix them. The use of lower level aggregated data and the analysis that takes into account spatial interactions thus become particularly relevant because it allows us to reveal the diversity of interactions at the micro-level.Research objective. This study aims to determine the significance of spatial relationships at different levels of data aggregation and hierarchical dependencies in per capita income and highlight the level of administrative division (regional or municipal) that has the greatest impact on per capita income.Methods and data. The analysis relies on the data from 2,270 municipalities in 85 Russian regions. The Hierarchical Spatial Autoregressive Model (HSAR) was used to distinguish both spatial and hierarchical effects. We used three specifications of the model: with estimates of the spatial interaction on the higher level (spatial error at the regional level), on the lower level (spatial lag at the municipal level), and on both levels.Results. Spatial interactions explain the observed variation of per capita income at the municipal level data at both the higher (regional) and lower (municipal) levels but the model with the estimated spatial interaction on the higher level was better.Conclusion. Despite the importance of spatial interactions at the lower level, models that take into account spatial interactions only at the upper level may better explain the observed differences in some cases. Our findings contribute to the rather scarce research literature on spatial relationships on several levels of administrative division. We have shown that for each specific case it is important to identify not only the factors but also the spatial effects in relation to this or that level of the territorial hierarchy

Isothiocyanates of phosphorus acids, N-phosphorylated thiocarbamates and thioureas

Current data on the synthesis, structures, the activities, and practical applications of the isothiocyanates of tri-coordinate, tetracoordinate, pentacoordinate, and hexacoordinate phosphorus acids and N-phosphorylated and N-thiophosphorylated thiocarbamates, dithiocarbamates, and thioureas are examined and surveyed. © 1985 IOP Publishing Ltd

Hierarchy of critical temperatures in four-layered ferromagnet/ superconductor nanostructures and control devices

The four-layered F/S/F′/S′ nanostructure consisting of rather dirty superconducting (S) and ferromagnetic (F) metals is studied within the theory of the proximity effect taking detailed account of the boundary conditions. The F/S structures with four F and S layers are shown to have considerably richer physics than the F/S/F trilayer (due to the interplay between the 0 and π phase superconductivity and the 0 and π phase magnetism) and even the F/S superlattices. The extra π phase superconducting states obtained for the four-layered F/S/F′/S′ system are found to be different from the known "superlattice" states. The dependence of the critical temperatures versus the F layer thicknesses is investigated. An optimal set of parameters is determined, for which the difference between the critical temperatures for different states becomes significant, and the corresponding phase diagrams are plotted. It is proven that this system can have different critical temperatures for different S and S′ layers. A conceptual scheme of a control device with superconducting and magnetic recording channels that can be controlled separately using a weak external magnetic field is proposed on the basis of the F/S/F′/S′ nanostructure. The devices with four, five, six, and seven different states are explored. © 2006 The American Physical Society

Dipole moments of organophosphorus compounds - Communication 2. Benzoylphosphonates, benzoylphosphinates, and benzoylphosphine oxides

1. Diethyl esters of certain substituted benzoylphosphonic acids and diethyl(diphenyl)benzoylphosphine oxides were synthesized, and their dipole moments were determined. 2. The steric structure of the investigated compounds was established. 3. Interaction of the substituents in the benzene ring of diethyl esters of benzoylphosphonic acids with the diethoxyphosphono group was detected. © 1971 Consultants Bureau

Reaction of sodium salts of dialkylphosphorous acids with carboxylic acid nitriles

The reaction of the Na salts of dialkylphosphorous acids with nitriles leads to the dialkyl esters of N-(1-dialkylphosphonylalkyl) amidophosphoric acids, whose formation proceeds via the aminophosphonate-amidophosphate rearrangement of the sodium derivatives of bis(dialkylphosphonyl)alkylamines. © 1978 Plenum Publishing Corporation

Decoupled superconductivity in the four- and five-layered ferromagnet-superconductor nanostructures and control devices

The ferromagnet/superconductor (F/S) tetra- and pentalayer consisting of rather dirty metals are considered with regard for the boundary conditions. The dependences of critical temperatures Tc versus the thicknesses of the F layers are investigated. The clearest manifestation of decoupled superconductivity for the F′/S′/F″/S″ tetralayer is the rise of a hierarchy of transition temperature Tc, and different S′ and S″ layers can have different critical temperatures. The same is valid for nonsymmetrical case of the F′/S′/F″/S″/ F‴ pentalayer. The complicated phase diagram of the tetralayer is discussed. The inverse action of superconductivity on magnetism leads to preferable mutual antiferromagnetic orientation of magnetizations of the F′ and F″ layers, if the inner S′ layer is in the superconducting state. Conceptual scheme of the new nanoelectronics control device, that has up to seven different states and combine in one sample the advantages of two different recording channels, is proposed. © 2005 Elsevier B.V. All rights reserved