Fractional dynamics of coupled oscillators with long-range interaction

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0相似文献   

EPR Spectroscopy of Impurity Thulium Ions in Yttrium Orthosilicate Single Crystals

The frequency-field and orientation dependences of the electron paramagnetic resonance (EPR) spectra are measured for impurity Tm³⁺ ions in yttrium orthosilicate (Y₂SiO₅) single crystals by stationary EPR spectroscopy in the frequency range of 50–100 GHz at 4.2 K. The position of the impurity ion in the crystal lattice and its magnetic characteristics are determined. The temperature dependences of the spin–lattice and phase relaxation times are measured by pulse EPR methods in the temperature range of 5–15 K and the high efficiency of the direct single-phonon mechanism of spin–lattice relaxation is established. This greatly shortens the spin–lattice relaxation time at low temperatures and makes impurity Tm³⁺ ions in Y₂SiO₅ a promising basis for the implementation of high-speed quantum memory based on rare-earth ions in dielectric crystals.     

High-Frequency EPR Spectroscopy of Tb3+ Ions in Synthetic Forsterite

Paramagnetic centers formed by the impurity Tb³⁺ ions in synthetic forsterite Mg₂SiO₄ have been studied by high-frequency tunable electron paramagnetic resonance spectroscopy in the frequency range of 150–300 GHz. These centers represent single Tb³⁺ ions and dimer associates of the Tb³⁺ ions. It has been found that the integral intensity of resonance transitions belonging to the dimer centers is much higher than that to be expected for the statistical distribution of the impurity Tb ions in the forsterite host. Therefore, there is a mechanism favoring the self-organization of the Tb ions in dimer associates during the crystal growth. The parameters of the effective spin Hamiltonian describing the dependence of electron-nuclear sublevels on the magnetic field have been determined for all observed paramagnetic centers and the possible structures of the centers have been discussed.     

Collapse and Revival of the Electron Spin Echo of Impurity Yb3+ Ions on Hidden Frequency Combs of Hyperfine Interactions in a Y2SiO5 Single Crystal

JETP Letters - The collapse and revival of Hahn electron spin echo signals excited on electron–nuclear spin levels of an impurity 173Yb3+ ion in yttrium orthosilicate Y2SiO5 have been...     

The Strong Thirteen Spheres Problem

The thirteen spheres problem asks if 13 equal-size non-overlapping spheres in three dimensions can simultaneously touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schütte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen-sphere problem (or the Tammes problem for 13 points), which calls for finding the maximum radius of and an arrangement for 13 equal-size non-overlapping spheres touching the unit sphere. In this paper, we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on an enumeration of irreducible graphs.     

True reference nanosensor realized with silicon nanowires

Conventional gate oxide layers (e.g., SiO(2), Al(2)O(3), or HfO(2)) in silicon field-effect transistors (FETs) provide highly active surfaces, which can be exploited for electronic pH sensing. Recently, great progress has been achieved in pH sensing using compact integrateable nanowire FETs. However, it has turned out to be much harder to realize a true reference electrode, which--while sensing the electrostatic potential--does not respond to the proton concentration. In this work, we demonstrate a highly effective reference sensor, a so-called reference FET, whose proton sensitivity is suppressed by as much as 2 orders of magnitude. To do so, the Al(2)O(3) surface of a nanowire FET was passivated with a self-assembled monolayer of silanes with a long alkyl chain. We have found that a full passivation can be achieved only after an extended period of self-assembling lasting several days at 80 °C. We use this slow process to measure the number of active proton binding sites as a function of time by a quantitative comparison of the measured nonlinear pH-sensitivities to a theoretical model (site-binding model). Furthermore, we have found that a partially passivated surface can sense small changes in the number of active binding sites reaching a detection limit of δN(s) ≈ 170 μm(-2) Hz(-1/2) at 10 Hz and pH 3.     

One-dimensional model of inhomogeneous shear in sliding

The paper briefly describes a one-dimensional dynamic model of plastic shear deformation in a material surface layer in sliding friction, giving grounds to the reduction of the problem dimension from 3D to 1D. A selection of simulation results is presented to illustrate the peculiarities of plastic deformation under the action of two competitive processes — work hardening and thermal softening due to frictional heating. Presented also are experimental data on which to base the conclusion on the possibility of surface layer flow similar to flow of a viscous fluid. To assess from the Reynolds number whether turbulization of the surface layer is feasible, simulation results are used.     

Molecular organization of reactants in the kinetics and catalysis of liquid phase reactions: IX. The catalytic assistance of an alcohol as a component of the medium in the aminolysis of esters

The kinetics of the reaction ofp-nitrophenyl acetate with n-butylamine is studied in various solvents containing n-butanol as a component of the medium. The alcohol is shown to assist the aminolysis by the participation in the proton transfer from the amine molecule to ester. The stoichiometric composition of the polymolecular complexes of amine with the alcohol participating in the reaction is found from the kinetic data at low concentrations of n-butanol and the data on its association in solutions. At high concentrations of the alcohol, the kinetic data are described within the framework of a model that assumes the participation in the reaction of hydroxy groups of the alcohol in the composition of alcohol clusters. The rate of the process is determined by the concentration and sizes of the clusters. The complex kinetics of the catalytic assistance of the alcohol as a component of the medium are quantitatively interpreted according to the concepts on the role of the structural organization of the liquid in the kinetics of molecular reactions in solutions.