In memory of Sergei A. Kornilov

Orbituary

In memory of Sergei A. Kornilov     

Selective synthesis of the C3v isomer of C60h18

[chemical structure: see text]. C60H18 has been produced by hydrogenation of C60 at 100 bar H2 pressure and 673 K for 10 h. We have investigated the crude material without any purification by use of 1H NMR, 13C NMR, and IR spectroscopy and Fourier transform ion cyclotron resonance mass spectrometry. We show that the crude material consists of 95% of the C3v isomer of C60H18.     

Total absorption of an electromagnetic wave by an overdense plasma

We show both theoretically and experimentally that an electromagnetic wave can be totally absorbed by an overdense plasma when a subwavelength diffraction grating is placed in front of the plasma surface. The absorption is due to dissipation of surface plasma waves (plasmons polaritons) that have been resonantly excited by the evanescent component of the diffracted electromagnetic wave. The developed theoretical model allows one to determine the conditions for the total absorption.     

Formation and composition of the clathrate phase in the H<Subscript>2</Subscript>O-H<Subscript>2</Subscript> system at pressures to 1.8 kbar

The transition of the hexagonal ice phase I_h to the clathrate phase sII has been found in the H₂O-H₂ system at a pressure of about 1 kbar under conditions of an excess of gaseous hydrogen. The pressures of the I_h → sII and sII → I_h transitions have been determined over a temperature range from ?36 to ?18°C, and the pressure dependence of the synthesis temperature of the clathrate phase from a liquid at pressures from 1.0 to 1.8 kbar has been constructed. The solubility of hydrogen in the I_h and sII phases and in liquid water has been measured. The concentration of hydrogen in the clathrate phase sII is about 1.2 wt % (10 mol %) near the boundary of the sII → I_h transition, and it increases to 2 wt % (16 mol %) at a pressure of 1.8 kbar.     

Tunable photon lifetime in photonic molecules: a concept for delaying an optical signal

We experimentally and theoretically studied the photon lifetime spectral distribution in two coherently coupled spherical microcavities of 3-16 microm diameter forming a photonic molecule, which shows a multipeak narrowband modal structure resulting from lifting of the mode degeneracy with respect to the azimuthal quantum number. The results demonstrate the feasibility of photonic molecules as a basis for a multichannel, wavelength-tunable optical delay-line device, which can be used for delay times in the range 10 ps to 1 ns.     

Exact Anomalous Dimensions of Composite Operators in the Obukhov–Kraichnan Model

We consider two stochastic equations that describe the turbulent transfer of a passive scalar field (x)(t,x) and generalize the known Obukhov–Kraichnan model to the case of a possible compressibility and large-scale anisotropy. The pair correlation function of the field (x) is characterized by an infinite collection of anomalous indices, which have previously been found exactly using the zero-mode method. In the quantum field formulation, these indices are identified with the critical dimensions of an infinite family of tensor composite operators that are quadratic in the field (x), which allows obtaining exact values for the latter (the values not restricted to the -expansion) and then using them to find the corresponding renormalization constants. The identification of the correlation function indices with the composite-operator dimensions itself is supported by a direct calculation of the critical dimensions in the one-loop approximation.     

Charge and orbital order in Fe3O4

Charge and orbital ordering in the low-temperature monoclinic structure of magnetite (Fe3O4) is investigated using the local spin density approximation with Coulomb interaction correction method. While the difference between t(2g) minority occupancies of Fe(2+)(B) and Fe(3+)(B) cations is large and gives direct evidence for charge ordering, the screening is so effective that the total 3d charge disproportion is rather small. The charge order has a pronounced [001] modulation, which is incompatible with the Anderson criterion. The orbital order agrees with the Kugel-Khomskii theory.     

On the Reflection Coefficient in a Superbarrier Passage of a Quantum Particle

The problem on the reflection coefficient is considered for a quantum particle passing over a potential barrier. A rigorous treatment of this problem is not available in the literature. We have developed a consecutive method of finding the pre-exponential multiplier in solving the problem on the probability of the passage in a quasiclassical case, including a correct choice of the singular point. Its novelty in comparison to the earlier used methods is that it involves some rules for the most expedient analytic continuation of the wave function to the complex region. Our method does not use the conventional subdivision of the incident wave function into two ones: penetrating and reflected. When considering the action integral L = pdx = L ₁ + iL ₂, we obtain a bundle of trajectories with L ₂ = const: one extreme member of this bundle is the real axis and the other extreme member is a curve which is indefinitely close to one of the singular points. This singular point plays the leaging role in finding the asymptote of the reflection coefficient R having a physical meaning. Five examples that explain the theory are considered.     

“Toy Models” of Turbulent Convection and the Hypothesis on Local Isotropy Restoration

We give a brief review of recent results devoted to effects of large-scale anisotropy on the inertial-range statistics of the passive scalar quantity (t, x) advected by a synthetic turbulent velocity field with covariance (t – t')|x – x'|. An inertial-range anomalous scaling behavior is established, and explicit asymptotic expressions for the structure functions S _n(r) [(t, x + r) – (t, x)] ⁿ are obtained; they are represented by superpositions of power laws with nonuniversal (dependent on the anisotropy parameters) anomalous exponents, calculated to the first order in in any space dimension. The exponents are associated with tensor composite operators, built of scalar gradients, and exhibit a kind of hierarchy related to the degree of anisotropy: the less the rank, the less the dimension and, consequently, the more important the contribution to the inertial-range behavior. The leading terms of even (odd) structure functions are given by scalar (respectively, vector) operators. Small-scale anisotropy reveals itself in odd correlation functions: for an incompressible velocity field, S ₃/S ₂ ^3/2 decreases in the direction toward the depth of the inertial range, while higher-order odd ratios increase; if the compressibility is sufficiently strong, the skewness factor also becomes increasing. Bibliography: 33 titles.