How Do Defects in Carbon Nanostructures Regulate the Photoinduced Electron Transfer Processes? The Case of Phenine Nanotubes

Photoinduced electron transfer is studied in a series of inclusion complexes of structurally modified phenine nanotubes ( pNT ) with C₇₀ using the TD-DFT method. Analysis of electronic properties of the complexes shows that the electron transfer is infeasible in pNT_4d⊃C₇₀ built on the tetrameric array of [6]cyclo-meta-phenylene ([6]CMP) units. However, replacing one or more [6]CMP units with a coronene moiety enables electron transfer from pNT to C₇₀ . The generation of the charge separated states from the lowest locally excited states occurs on a sub-nanosecond time scale. Depending on the number of the [6]CMP units, the charge recombination rate varies from 1.8 ⋅ 10⁷ to 3.1 ⋅ 10² s⁻¹, i. e., five orders of magnitude.     

Asymmetric Hubbard model in the generating functional method: Spectral functions in the Falicov-Kimball limit

In the framework of the dynamical mean field theory, we investigate the densities of states of the fermionic and bosonic branches of the spectrum of the asymmetric Hubbard model, which is used to describe a strongly correlated two-sort (A, B) system of fermions (electrons). To solve the effective one-site problem, we develop an approximate analytic approach based on the Kadanoff-Baym generating functional method. This technique allows constructing the irreducible part (the mass operator) of the particle Green’s function in the form of a formal expansion in powers of the coherent potential. In the first order, the scheme reproduces the so-called generalized approximation Hubbard-III. To improve it, we develop a self-consistent method for calculating both the fermionic and bosonic Green’s functions. As U → ∞ in the Falicov-Kimball limit for the asymmetric Hubbard model, when the particles of sort B become localized, we find the spectral densities ρ_B and ρ_AB of states of both branches and consider the changes of their forms depending on temperature and particle concentrations. Comparing with the exact thermodynamic dependences μ_B(n_B), we establish the applicability limits of the self-consistent generalized approximation Hubbard-III. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 164–182, January, 2008.     

A study of the perturbed stress state of a closed cylindrical shell with a system of part-through transverse cracks

We study the elastic equilibrium of a closed infinite circular cylindrical shell with a system of surface cracks of identical length and depth. We use the method of singular integral equations together with the modeling of solid matter in the plane of a part-through crack by irregularly distributed “line springs”. We conduct a numerical analysis of the variation of the relative stress intensity factor at the center of a crack as a function of the parameters of a crack and the number of cracks. We study cracks located on both the interior and exterior surface of the shell. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 63–65.     

The perturbed stress state of a closed cylindrical shell with longitudinal cracks on its inner surface

Using the Rice-Levy line spring model we find an approximate solution of the problem of elastic balance of a closed infinite circular cylindrical shell weakened by a periodic system of longitudinal interior cracks of identical length. The stress intensity factors are found at the center of a crack for various numbers of cracks with various parameters. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Approximation characteristics of the classes B p,θ Ω of periodic functions of many variables

We obtain exact order estimates for the approximation of the classes B _p,θ ^Ω of periodic functions of many variables in the space L _q by using operators of orthogonal projection and linear operators satisfying certain conditions. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 692–704, May, 2006.