Three-dimensional two-phase filtration in an imperfect borehole in an oil-bearing stratum

The method of zonal linearization [1] is applied to the solution of the three-dimensional problem of the combined filtration of petroleum and bottom water to a borehole which is imperfect in the degree of opening up of the stratum. The article gives a system of integro-differential equations of the dynamics of surfaces of equal saturation (isosats), which is valid both for the waterless period of the work of the work of the borehole, and for the period of progressive flooding. A numerical solution of the problem is obtained, which is compared with an approximate analytical solution.     

Marcinkiewicz exponents and their application in boundary-value problems

We introduce certain new characteristics for non-rectifiable curves which allow to sharpen known solvability conditions for so-called jump boundary-value problems on that curves.     

Integration over Nonrectifiable Paths with Applications

We study a generalized contour integral along a nonrectifiable path and its applications.

     

Isotropic and antisymmetric double-exchange, zero-field, Zeeman, and hyperfine splittings in trinuclear valence-delocalized [Cu3(7+)] clusters

Valence delocalization in the [Cu3(7+)] trimer is considered in the model of the double-exchange coupling, in which full delocalization corresponds to the migration of the single d(x2-y2) hole and relatively strong isotropic double-exchange coupling. Strong double exchange results in the pairing of the individual spins in the delocalized trimer even at room temperature. The model explains the delocalized singlet 1A1 ground state in the planar Cu3(mu3-O) core by strong double exchange with positive double-exchange parameter t(0), whereas the delocalized triplet ground state of the [Cu3(7+)] trimer, which was observed in the Cu3(mu3-S)2 cluster, may be explained by the double exchange with relatively weak positive t(0): 0 < t(0) < 2J (degenerate 3E ground state) or negative t(0) (triplet 3A2 ground state). An analysis of the splitting of the delocalized degenerate 3E term requires inclusion of the antisymmetric double-exchange interaction, which takes into account the spin-orbit coupling in the double-exchange model. The cluster parameter KZ of the antisymmetric double-exchange coupling is proportional to t(0) and anisotropy of the g factor Deltag(parallel)[Cu(II)], KZ < t(0). Antisymmetric double exchange is relatively large in the [Cu3(7+)] cluster with the d(x2-y2) magnetic orbitals lying in the Cu3 plane [Cu3(mu3-O) core], whereas for the d(x2-y2) magnetic orbitals lying in the plane perpendicular to Cu3, antisymmetric double-exchange coupling is weak [Cu3(mu3-S)2 cluster]. The antisymmetric double-exchange coupling results in the linear zero-field splitting DeltaK = 2[equation: see text]KZ (approximately t(0)) of the delocalized degenerate 3E term that leads to strong anisotropy of the Zeeman splittings in the external magnetic field and a complex electron paramagnetic resonance (EPR) spectrum. The delocalized model of hyperfine interaction explains the hyperfine structure [10 hyperfine lines with the relative intensities 1:3:6:10:12:12:10:6:3:1 and the interval a/3] of the EPR transitions in the triplet states that was observed in the EPR spectra of the Cu3(mu3-S)2 cluster.     

Optical properties of individual GaAs quantum dots embedded into AlGaAs nanowires

The photoluminescence (PL) spectra of semiconductor structures, namely, Al_0.3Ga_0.7As-based quasi-one-dimensional cylindrical nanowires (nanowhiskers), are measured. The diameter of a typical nanowire is 20–50 nm, and its length was 0.5–1.0 μm. Samples containing one or several GaAs-based quantum dots at the center of the quantum wire are studied. The dot thickness is 2 nm, and the dot diameter is 15–40 nm. Individual nanowhiskers, several nanowhiskers (3–4), and ensembles consisting of many nanowhiskers are studied. The PL spectra are measured for different optical-excitation intensities and in magnetic fields of up to 11 T.     

The Effect of Ionizing Preirradiation of Energy-Saturated Materials on Their Susceptibility to Irradiation with a High-Current Electron Beam

The susceptibility of two types of energy-saturated materials (composition VS-2, which is an energy-saturated metal-inorganic compound with minor additions of a polymer binder, and an energy-saturated composite of NCP and fullerene) preirradiated with β particles and γ quanta to irradiation with a high-current nanosecond electron beam is studied. The obtained results demonstrate that the preirradiated energy-saturated materials are significantly more susceptible to electron irradiation. This effect lasts for at least eight months and is more pronounced in the case of gamma-preirradiation.     

Quadrupolar forces and aggregation of nematic droplets

The electrostatic quadrupolar interaction between spherical nematic droplets in an isotropic (and nonconducting) liquid is calculated. It is found to have an anisotropic form U _q ∝1/R ⁵, where R is the distance between droplets, with repulsion for droplets having parallel orientation of the quadrupole moments and attraction at oblique angles around the orthogonal orientation. In an external magnetic field aligning the orientations of the quadrupole moments, a competition of the quadrupolar repulsion and van der Waals attraction (U _vdW∝ 1/R ⁶) leads to a specific spatial organization of droplets which is in fact often reported in experimental observations (see the monograph by P. Drzaic, Liquid Crystal Dispersions, World Scientific, Singapore (1995) and references cited therein). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 747–752 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Photocatalytic oxidation of cyclohexane by atmospheric oxygen in CH2Cl2 in the presence of an oxometallate-tetraalkylammonium system

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2390–2391, October, 1989.