Planarity takes over in the C(x)H(x)P(6-x) (x = 0-6) series at x = 4

In this work we examine a structural transition from non-planar three-dimensional structures to planar benzene-like structures in the C(x)H(x)P(6-x) (x = 0-6) series. The global minima of P(6), CHP(5), and C(2)H(2)P(4) species are benzvalene-like structures. The benzvalene and benzene-like structures of C(3)H(3)P(3) are close in energy with the former being slightly more stable at our best level of theory. The transition occurs at x = 4 (C(4)H(4)P(2)), where the benzene-like structures become significantly more stable than the benzvalene-like structures. We show that the pseudo Jahn-Teller effect, which is responsible for the deformation of planar P(6), CHP(5), and C(2)H(2)P(4) structures, is completely suppressed at x = 3 (benzene-like structures of C(3)H(3)P(3)). We present NICS(zz) values of all the benzene-like isomers in the series.     

Molecular wheel to monocyclic ring transition in boron-carbon mixed clusters C2B6⁻ and C3B5⁻

In this joint experimental and theoretical work we present a novel type of structural transition occurring in the series of C(x)B(8-x)(-) (x=1-8) mixed clusters upon increase of the carbon content from x=2 to x=3. The wheel to ring transition is surprising because it is rather planar-to-linear type of transition to be expected in the series since B(8), B(8)(-), B(8)(2-) and CB(7)(-) are known to possess wheel-type global minimum structures while C(8) is linear.     

Pore-Scale Investigation of Two-Phase Flows in Three-Dimensional Digital Models of Natural Sandstones

The results of numerical simulation of the processes of two-phase flow through a porous medium in three-dimensional digital models of the porous space of three natural sandstone samples are given. The calculations are carried out using the lattice Boltzmann equations and the digital field gradient model over a wide range of the capillary numbers and the viscosity ratios of injected and displaced fluids. The conditions of flow through a porous medium with capillary fingering, viscous fingering and with stable displacement front are revealed.     

EPR investigation of the spin-spin interactions in a Cu(II)-Gd(III)-Fe(III) heterospin system

The spin-spin interactions in a system that contains three different spin carriers, [{LCu}Gd(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O (1) [L²⁻, N,N-propylenedi(3-methoxysalicylideneiminato)], were investigated by electron paramagnetic resonance spectroscopy. Additional information was obtained by analyzing the discrete heterobinuclear system [LCu(OH₂)Gd(O₂NO)₃] (2), which contains the Cu(II)-Gd(III) pair also existing in the structure of 1, and the compounds [{LCu}Gd(H₂O)₃{Co(CN)₆}] _n ·3.5nH₂O and [{LCu}La(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O, which are isostructural with 1 and in which the paramagnetic low-spin Fe(III) and Gd(III) ions were replaced by diamagnetic low-spin Co(III) and La(III), respectively. The investigations were carried out in the temperature range of 293–4 K in both X- and Q-bands and also using a dual-mode X-band. The experimental spectra of the Cu(II)-Gd(III) pairs in 2 were interpreted as the sum of spectra of the ground spin state with total S = 4 and the excited state with S = 3 appearing due to the ferromagnetic exchange interaction between Cu(II) and Gd(III) ions. By fitting the experimental and simulated spectra, the zero-field splitting parameters of the Gd(III) ion are estimated and it is shown that no influence of the anisotropic interaction is detected. The magnetic properties of 1 are discussed from the perspective of the interaction of the Cu(II)-Gd(III) binuclear fragments with the Fe(III) ions.     

Ferromagnetic Interaction between Copper and Terbium Ions in Pentanuclear Cluster [Cu3Tb2(ClCH2COO)12(H2O)8] · 2H2O

For the first time the exchange interaction between copper and non-Kramers Tb³⁺ ions was studied by means of electron paramagnetic resonance (EPR). Features of the manifestation of this interaction in the EPR spectra of dimer fragments Cu–Tb and pentanuclear fragments Cu–Tb–Cu–Tb–Cu are analyzed. The possibility to determine the sign and value of this interaction from EPR spectra for the case when the lowest states of Tb³⁺ are the states |0〉, | ± 1〉 is shown. The exchange interaction between copper and trivalent terbium ions in the studied pentanuclear complex is ferromagnetic. Authors' address: Violeta K. Voronkova, Kazan Physical-Technical Institute, Russian Academy of Sciences, Sibirsky trakt 10/7, Kazan 420029, Russian Federation     

Electro-elastic interactions and second order anisotropic constitutive equations

Piezoelectricity is usually expressed as an interaction between mechanical and electrical variables. The physics involved is hence governed by a coupling between Maxwell's equations of electromagnetism and the equations of elasticity. Such a coupling takes us through the piezoelectric constitutive relations. In this work, the second order anisotropic constitutive equations are treated, and in particular, the number of independent material constants is computed for all the 32 crystallographic classes.Paper presented, in reduced version, at the 12th Italian National Congress of Theoretical and Applied Mechanics (AIMETA '95), October 1995, Naples, Italy.     

Mathematical modeling of the accuracy characteristics in problems of precision quantum tomography of biphoton states

A model that approximately takes into account instrumental errors in problems of precision reconstruction of quantum states is considered. The model is based on the notion of coherence volume, which characterizes the quality of the experimental and technological realization of the measurement protocol of a quantum state. Various sources of instrumental errors that affect the reconstruction accuracy of quantum states are mathematically modeled. It is shown that, for precision tomography of quantum states, one should take into account random coincidences that occur because the operating time of the photon detection system is finite. Among other possible sources of instrumental errors of the measurement protocol, one should take into account errors of the rotation angles and optical thicknesses of polarization plates, a possible drift in the parameters of the pump laser, and so on.     

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are δ2 =4.69 and δ4 = 4.6, which are comparable with the theoretical asymptotic value δ=4.669.     

Aerosol aspiration into a cylindrical sampler from a low-velocity downward flow and from calm air

The problem of aerosol aspiration into a two-dimensional cylindrical sampler from a low-velocity downward flow and from calm air is solved. A simple analytical model for the velocity field of the carrier medium in the vicinity of the sampler with allowance for the finite size of the input orifice is proposed. Parametric studies of the aspiration factor as a function of the Stokes number for different ratios of the free-stream and aspiration velocities and different gravity-induced sedimentation velocities for two positions of the sampler are performed. Sedimentation of particles on the lower side of the cylinder for the sampler with a downward-oriented orifice is discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 122–129, March–April, 2005.