Nonlinear effects in gas filtration

The existence of considerable deviations from the linear Darcy filtration law has been established for numerous systems consisting of a fluid and a porous medium. One of the manifestations of this nonlinearity is the existence of a limiting (initial) pressure gradient—the minimum value of the pressure gradient for which fluid motion occurs. (As a rule, fluid motion still takes place for subcritical values of the pressure gradient, but very slowly; on reaching the limiting value of the pressure gradient there is a marked acceleration of the filtration. The limiting-gradient concept thus provides a good approximation for velocities which are not too low.)We would also expect nonlinear effects in the motion of a Newtonian liquid or gas in a porous medium containing some amount of fluid which does not participate in the main motion. These effects can take the form of layers enclosing the particles of the porous medium and partly or completely blocking the pore channels. For sufficiently high pressure gradients rearrangement of these layers must begin, accompanied by a change of the hydrodynamic resistance of the porous medium.As a result of this restructuring it is natural to expect a disproportionately fast increase of the filtering-fluid flow rate with increase of the pressure differential; i.e., the filtration law of a Newtonian fluid in a medium containing a. layer of bound fluid having elasticity will have the form which is characteristic for pseudoplastic non-Newtonian fluids. In particular, if the initial attached-fluid content is so large that all the pore channels are blocked in the initial state, then the motion of the liquid (gas) being externally pumped begins only after the attached fluid layers are partly ruptured. Therefore, under these conditions the appearance of a limiting (initial) pressure gradient for filtration of a Newtonian fluid is possible. This can occur in filtration of a gas in argillous rocks containing connate water, since the water and the clay particles form a colloidal suspension which has some shear strength.This phenomenon may be of importance in the development of gas deposits which are associated with argillous rocks, particularly in determining the possible current and final gas yield. In fact, the most characteristic property of flows with an initial gradient is the formation of impermeable blocks; if the deposits have the usual nonuniformity the incompleteness of the gas extraction from the reservoir will manifest itself in both microscopic and macroscopi scales.In the following study we present relations describing gas filtration under such conditions and results of laboratory experiments which confirm the concepts described. Hydrodynamic estimates are also made of the possible effects of the initial gradient.The authors wish to thank I. I. Eremina for assistance in making the calculations, A. Sh. Asadov and Sh. S. Aslanov for assistance in conducting the experiments.     

Representation of square matrices by the product of diagonal,orthogonal, triangular,and integral unimodular matrices (in connection with the inhomogeneous Minkowski conjecture)

It is shown that for all sufficiently large numbers n nonsingular square matrices of order n are found for which the representation indicated in the title is impossible.Translated by L. Guy and J. P. Jones.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 67, pp. 86–94, 1977.In closing, I express deep gratitude to B. F. Skubenko for posing the problem and his attention to the work, and also to L. V. Kuz'min and A. V. Malysev for remarks and assistance in the final formulation of this paper.     

Adsorption-energetic and IR spectroscopic studies of NH4 natrolite

The ammonium form of natural zeolite, natrolite, obtained by vapor phase ion exchange is similar to calcium-containing zeolites of the natrolite group in its de- and rehydration characteristics and the heats of immersion in water. The adsorption capacity and the heat of immersion in water are maximum after evacuation of the zeolite at 200 °C. The irreversible sintering of NH₄ natrolite occurs above 200 °C (up to 45% at 500 °C), accompanied by the formation of hydroxyl groups. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 359–361, February, 1998.     

Duality in left-right symmetric seesaw mechanism

We consider type I + II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m(v) and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution [symbol: see text] = m(v)/nu(L) - f, where nu(L) is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2(n). We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f.     

Factorization of proper holomorphic maps on irreducible bounded symmetric domains of rank≥2

We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described.     

Technology of manufacturing micropixel avalanche photodiodes and a compact matrix on their basis

A technology for manufacturing a new micropixel avalanche photodiode (MAPD) with deeply buried pixels (including two epitaxial layers between which an array of n ⁺) regions is formed by ionic doping) is described. A new method for manufacturing the compact MAPD matrices with minimum dead zone is proposed.     

Regioselective Amine–Borane Cyclization: Towards the Synthesis of 1,2‐BN‐3‐Cyclohexene by Copper‐Assisted Triazole/Gold Catalysis

The combination of triazole/gold (TA‐Au) and Cu(OTf)₂ is identified as the optimal catalytic system for promoting intramolecular hydroboration for the synthesis of a six‐membered cyclic amine–borane. Excellent yields (up to 95 %) and regioselectivities (5‐exo vs. 6‐endo) were achieved through catalyst control and sequential dilution. Good functional‐group tolerance was attained, thus allowing the preparation of highly functionalized cyclic amine–borane substrates, which could not be achieved using other methods. Deuterium‐labeling studies support the involvement of a hydride addition to a gold‐activated alkyne with subsequent C?B bond formation.     

Structural elucidation of nitro-substituted five-membered aromatic heterocycles utilizing GIAO DFT calculations

The GIAO (Gauge Including Atomic Orbitals) DFT (Density Functional Theory) method is applied at the B3LYP/6-31+G(d,p)//B3LYP/6-31+G(d), B3LYP/6-311++G(d,p)//B3LYP/6-31+G(d), B3LYP/6-311+G (2d,p)//B3LYP/6-31+G(d) and B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) levels of theory for the calculation of proton and carbon chemicals shifts and coupling constants for 25 nitro-substituted five-membered heterocycles. Difference (1D NOE) spectra in combination with long-range gHMBC experiments were used as tools for the structural elucidation of nitro-substituted five-membered heterocycles. The assigned NMR data (chemical shifts and coupling constants) for all compounds were found to be in good agreement with theoretical calculations using the GIAO DFT method. The magnitudes of one-bond (1JCH) and long-range (nJCH, n>1) coupling constants were utilized for unambiguous differentiation between regioisomers of nitro-substituted five-membered heterocycles.