A hierarchy of integrable partial differential equations in 2+1 dimensions associated with one-parameter families of one-dimensional vector fields

We introduce a hierarchy of integrable partial differential equations in 2+1 dimensions arising from the commutation of one-parameter families of vector fields, and we construct the formal solution of the associated Cauchy problems using the inverse scattering method for one-parameter families of vector fields. Because the space of eigenfunctions is a ring, the inverse problem can be formulated in three distinct ways. In particular, one formulation corresponds to a linear integral equation for a Jost eigenfunction, and another formulation is a scalar nonlinear Riemann problem for suitable analytic eigenfunctions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 147–156, July, 2007.     

Double clathrate hydrates of tetrabutylammonium fluoride + helium, neon, hydrogen and argon at high pressures

Decomposition curves of double ionic clathrate hydrates of tetrabutylammonium fluoride with helium, neon, hydrogen and argon were studied at pressures up to 800 MPa. Formation of double hydrates with helium, neon and hydrogen does not lead to any significant increase of the temperatures of decomposition of these hydrates; at high temperatures the hydrates may decompose even at lower temperatures than the hydrate of pure tetraalkylammonium salt does. Decomposition temperatures of double hydrates with argon in all cases were 4–8 °C higher in comparison with the decomposition temperature of ionic clathrate hydrates of tetrabutylammonium fluoride. We suppose that this behavior is caused by simultaneous effect of three factors on hydrate decomposition temperature: (1) partial filling of the small cavities in the framework of the hydrate with water molecules, (2) weakness of the van der Waals interactions between the gas molecules and the host water molecules, and (3) dissolution of helium, hydrogen and neon in the solution of tetrabutylammonium salt causing a decrease of melting temperatures of the hydrates formed from these solutions.     

Phase diagram and high-pressure boundary of hydrate formation in the ethane-water system

Dissociation temperatures of gas hydrate formed in the ethane-water system were studied at pressures up to 1500 MPa. In situ neutron diffraction analysis and X-ray diffraction analysis in a diamond anvil cell showed that the gas hydrate formed in the ethane-water system at 340, 700, and 1840 MPa and room temperature belongs to the cubic structure I (CS-I). Raman spectra of C-C vibrations of ethane molecules in the hydrate phase, as well as the spectra of solid and liquid ethane under high-pressure conditions were studied at pressures up to 6900 MPa. Within 170-3600 MPa Raman shift of the C-C vibration mode of ethane in the hydrate phase did not show any discontinuities, which could be evidence of possible phase transformations. The upper pressure boundary of high-pressure hydrate existence was discovered at the pressure of 3600 MPa. This boundary corresponds to decomposition of the hydrate to solid ethane and ice VII. The type of phase diagram of ethane-water system was proposed in the pressure range of hydrate formation (0-3600 MPa).     

New type of phase transformation in gas hydrate forming system at high pressures. Some experimental and computational investigations of clathrate hydrates formed in the SF6-H2O system

In this work, we present a new, previously unknown type of structure transformation in the high-pressure gas hydrates, which is related to the existence of two different isostructural phases of the sulfur hexafluoride clathrate hydrates. Each of these phases has its own stability field on the phase diagram. The difference between these hydrates consists of partial filling of small D cages by SF(6) molecules in the high-pressure phase; at 900 MPa, about half of small cages are occupied. Our calculations indicate that the increase of population of small cavities is improbable, therefore, at any pressure value, a part of the cavities remains vacant and the packing density is relatively low. This fact allowed us to suppose the existence of the upper pressure limit of hydrate formation in this system; the experimental results obtained confirm this assumption.     

Initial-Boundary Value Problems for Linear and Soliton PDEs

We consider evolution PDEs for dispersive waves in both linear and nonlinear integrable cases and formulate the associated initial-boundary value problems in the spectral space. We propose a solution method based on eliminating the unknown boundary values by proper restrictions of the functional space and of the spectral variable complex domain. Illustrative examples include the linear Schrödinger equation on compact and semicompact n-dimensional domains and the nonlinear Schrödinger equation on the semiline.     

Model-independent quantum approach for intense laser detachment of a weakly bound electron

We present a model-independent theory for laser detachment of a weakly bound electron having a nonzero angular momentum. Our treatment reduces to the well-known Keldysh result for tunnel ionization upon neglecting rescattering effects. Numerical results for the above-threshold detachment spectrum of a negative ion having an outer p electron show significant modification of the rescattering plateau as compared to that for an ion having an outer s electron.     

Reaction of dichlorosilanes with lithium in the presence of arylethylenes

The reaction of organodichlorosilanes (RR'Sil₂ and RSiHCl₂) and mono- or diarylethylenes with metallic lithium in tetrahydrofuran gives the corresponding substituted silacyclopentanes in 25–75% yield. The general character of the reaction is demonstrated and the optimal conditions are found. The suggested structure is completely confirmed by a study of certain physical and chemical properties of the aryl-substituted silacyclopentanes. IR and NMR spectra are presented. It has been demonstrated by gas-liquid chromatography and NMR spectroscopy that the x, x-diaryl-1,1-dialkyl-silacyclopentanes formed from RR'SiCl₂ ArCH=CH₂ and lithium contain several possible isomers, which result from the position of the aryl substituents relative to one another or to the plane of the salicyclopentane ring.Part of M. N. Manakov's dissertation [1].The authors express their sincere thanks to V. A. Shlyapochnikov, L. A. Leites, E. D. Lubuzh, V. I. Sheichenko, and S. V. Shlyapnikov for help in the spectroscopic and chromatographic analysis.     

Threshold-related enhancement of the high-energy plateau in above-threshold detachment

We present nonperturbative theoretical results showing a resonant-like enhancement of above-threshold detachment spectra in the region of the high-energy plateau as the laser intensity sweeps across channel thresholds. This enhancement has a pure quantum origin stemming from well-known threshold phenomena in multichannel problems whose features are clearly demonstrated in our numerical results. Similar well-known anomalies at neutral atom thresholds are expected to explain experimentally observed resonant-like enhancements of above-threshold ionization spectra.