Difference schemes for the dirichlet problem for an elliptical equation with discontinuous coefficients in an arbitrary region on a regular grid

Exact difference scheme operators are used to construct a difference scheme for a second-order elliptical equation with discontinuous coefficients. The solution of the scheme converges to the solution of the original problem at a rate O(h^1/2) in the grid norm W₂ ¹().Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 3–7, 1985     

Formation of low-temperature deformation-induced segregations of nickel in Fe–Ni-based austenitic alloys

ABSTRACT

The authors present the results of an investigation in Fe–Ni-Cr austenitic alloys of the low-temperature deformation-induced segregations of nickel that form in the micro regions being (i) located close to grain- and subgrain boundaries and (ii) characteristic of the concentration and magnetic inhomogeneities indicated by the appearance of a dark diffraction contrast at the electron diffraction patterns taken from these regions typical (at the same time) of an enhanced value of Curie temperature. The observed effects were connected with the micro distortions caused by the local change of lattice parameter because of an increase in nickel concentration, as well as in the result of a magnetostriction dilatation. Using methods of the X-ray energy dispersive spectroscopy (XEDS) and atomic-probe body-section radiography (tomography – APT) has made it possible to determine the borders of those regions of austenite that were characteristic of an enhanced concentration of nickel in the fields of the localisation of a deformation-induced segregation of nickel in the vicinity of grain (subgrain) boundaries of austenitic alloys of the types Fe–13Cr–30Ni and Fe–37Ni–3Ti.     

Accuracy bound of the grid method in optimal control problem for elliptic systems

A rate of convergence bound compatible with the smoothness of the solution of the original differential problem is obtained for the grid method in the optimal control problem for elliptic systems with solutions in W₂ ²(D).Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 12–19, 1987.     

Disintegration of Ar N,Kr N,and (N2) N clusters during collisions with highly vibrationally excited SF6 molecules

It is shown that, when highly vibrationally excited SF₆ molecules (with vibrational energy E _vib ≥ 0.5–2 eV) collide with weakly bound van der Waals Ar _N , Kr _N , or (N₂) _N (N ≤ 30–40 atoms in a cluster) clusters in intersecting molecular and cluster beams, the molecules are trapped by the clusters, the clusters then undergo full disintegration, and the trapped molecules become free. The method of studying this process and the results obtained are described. The possibilities of application of this method for selective doping of clusters by molecules, laser separation of isotopes, and selective transportation of molecules to a surface are discussed.     

Determination of the composition and content of pulsed cluster beams from time-of-flight mass spectra of cluster fragments

The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.     

Measurement of nanoparticle temperature in a (CO2) N cluster beam using SF6 molecules as tiny probe thermometers

A temperature measurement technique using SF₆ molecules as tiny probe thermometers is described, and results are presented, for large (CO₂) _N van der Waals clusters (with N ≥ 10²) in a cluster beam. The SF₆ molecules captured by (CO₂) _N clusters in crossed cluster and molecular beams sublimate (evaporate) after a certain time, carrying information about the cluster velocity and internal temperature. Experiments are performed using detection of these molecules with an uncooled pyroelectric detector and infrared multiphoton excitation. The multiphoton absorption spectra of molecules sublimating from clusters are compared with the IR multiphoton absorption spectra of SF₆ in the incoming beam. As a result, the nanoparticle temperature in the (CO₂) _N cluster beam is estimated as T _cl < 150 K. Time-of-flight measurements using a pyroelectric detector and a pulsed CO₂ laser are performed to determine the velocity (kinetic energy) of SF₆ molecules sublimating from clusters, and the cluster temperature is found to be T _cl = 105 ± 15 K. The effects of various factors on the results of nanoparticle temperature measurements are analyzed. The potential use of the proposed technique for vibrational cooling of molecules to low temperatures is discussed.     

Encapsulation of cyanometalates by a tris-macrocyclic ligand tricopper(II) complex: syntheses, structural variation, and magnetic exchange coupling pathways

The reaction of [M(CN)(6)](3-) (M = Cr(3+), Mn(3+), Fe(3+), Co(3+)) and [M(CN)(8)](4-/3-) (M = Mo(4+/5+), W(4+/5+)) with the trinuclear copper(II) complex of 1,3,5-triazine-2,4,6-triyltris[3-(1,3,5,8,12-pentaazacyclotetradecane)] ([Cu(3)(L)](6+)) leads to partially encapsulated cyanometalates. With hexacyanometalate(III) complexes, [Cu(3)(L)](6+) forms the isostructural host-guest complexes [[[Cu(3)(L)(OH(2))(2)][M(CN)(6)](2)][M(CN)(6)]][M(CN)(6)]30 H(2)O with one bridging, two partially encapsulated, and one isolated [M(CN)(6)](3-) unit. The octacyanometalates of Mo(4+/5+) and W(4+/5+) are encapsulated by two tris-macrocyclic host units. Due to the stability of the +IV oxidation state of Mo and W, only assemblies with [M(CN)(8)](4-) were obtained. The Mo(4+) and W(4+) complexes were crystallized in two different structural forms: [[Cu(3)(L)(OH(2))](2)[Mo(CN)(8)]](NO(3))(8)15 H(2)O with a structural motif that involves isolated spherical [[Cu(3)(L)(OH(2))](2)[M(CN)(8)]](8+) ions and a "string-of-pearls" type of structure [[[Cu(3)(L)](2)[M(CN)(8)]][M(CN)(8)]](NO(3))(4) 20 H(2)O, with [M(CN)(8)](4-) ions that bridge the encapsulated octacyanometalates in a two-dimensional network. The magnetic exchange coupling between the various paramagnetic centers is characterized by temperature-dependent magnetic susceptibility and field-dependent magnetization data. Exchange between the CuCu pairs in the [Cu(3)(L)](6+) "ligand" is weakly antiferromagnetic. Ferromagnetic interactions are observed in the cyanometalate assemblies with Cr(3+), exchange coupling of Mn(3+) and Fe(3+) is very small, and the octacoordinate Mo(4+) and W(4+) systems have a closed-shell ground state.     

Tuning of inter- versus intrachain magnetic interactions in cyano-bridged Ni(II)/M(III) (M = Cr, Fe, Co) chain complexes

The reaction of [M(CN)6]3- (M = Cr3+, Fe3+, Co3+) with the nickel(II) complex of 2,4-diamino-1,3,5-triazin-6-yl-{3-(1,3,5,8,12-pentaazacyclotetradecane)} ([NiL]2+) in excess of ANO3 or ACl (A = Li+, Na+, K+, Rb+, Cs+, NH4+) leads to the cyano-bridged dinuclear assemblies A{[NiL][M(CN)6]}.xH2O (x = 2-5). X-ray structures of Li{[NiL][Cr(CN)6]}.5H2O, NH4{[NiL][Cr(CN)6]}.3.5H2O, K{[NiL][Cr(CN)6]}.4H2O, K{[NiL][Fe(CN)6]}.4H2O, Rb{[NiL][Fe(CN)6]}.3.5H2O, and Cs{[NiL][Fe(CN)6]}.3.5H2O, as well as the powder diffractometry of the entire Fe(III) series, are reported. The magnetic properties of the assemblies are dependent on the monocation A and discussed in detail. New efficient pathways for ferromagnetic exchange between Ni(II) and Fe(III) or Cr(III) are demonstrated. Field dependencies of the magnetization for the Fe(III) samples at low temperature and low magnetic field indicate a weak interchain antiferromagnetic coupling, which is switched to ferromagnetic coupling at increasing magnetic field (metamagnetic behavior). The interchain magnetic coupling can be tuned by the size of the A cations.