Derivation of the Gutenberg-Richter Empirical Formula from the Solution of the Generalized Logistic Equation

We have written a new equation to study the statistics of earthquake distributions. We call this equation "the generalized logistic equation". The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case in approximation of large magnitudes. To illustrate how the found solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N-25N, 5W-35W), Canary Islands, Magellan Mountains (20N-9S, 148E-170E), and the Sea of Japan. This approximation showed the excellent fit between the theoretical curves and observed data for earthquake magnitudes 1<m<9.Comment: 10 pages, 2 figures, 1 table, 8 references. Submitted to Natural Science, Earthquakes special issu

On the phonon-induced superconductivity of disordered alloys

A model of alloy is considered which includes both quenched disorder in the electron subsystem (``alloy'' subsystem) and electron-phonon interaction. For given approximate solution for the alloy part of the problem, which is assumed to be conserving in Baym's sense, we construct the generating functional and derive the Eliashberg-type equations which are valid to the lowest order in the adiabatic parameter.The renormalization of bare electron-phonon interaction vertices by disorder is taken into account consistently with the approximation for the alloy self-energy. For the case of exact configurational averaging the same set of equations is established within the usual T-matrix approach. We demonstrate that for any conserving approximation for the alloy part of the self-energy the Anderson's theorem holds in the case of isotropic singlet pairing provided disorder renormalizations of the electron-phonon interaction vertices are neglected. Taking account of the disorder renormalization of the electron-phonon interaction we analyze general equations qualitatively and present the expressions for $T_{c}$ for the case of weak and intermediate electron-phonon coupling. Disorder renormalizations of the logarithmic corrections to the effective coupling, which arise when the effective interaction kernel for the Cooper channel has the second energy scale, as well as the renormalization of the dilute paramagnetic impurity suppression are discussed.Comment: 59 pages, 10 Eps figures, LaTe

Electric-field-induced monoclinic phase in (Ba,Sr)TiO3_3 thin film

We have studied electric-field-induced symmetry lowering in the tetragonal (001)-oriented heteroepitaxial (Ba$_{0.8}$Sr$_{0.2}$)TiO$_3$ thin film deposited on (001)MgO substrate. Polarized micro-Raman spectra were recorded from the film area in between two planar electrodes deposited on the film surface. Presence of \textit{c}-domains with polarization normal to the substrate was confirmed from polarized Raman study under zero field, while splitting and hardening of the \textit{E}(TO) soft mode and polarization changes in the Raman spectra suggest monoclinic symmetry under external electric field

First-principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: Dynamical Mean-field Theory

A recently developed dynamical mean-field theory in the iterated perturbation theory approximation was used as a basis for construction of the "first principles" calculation scheme for investigating electronic structure of strongly correlated electron systems. This scheme is based on Local Density Approximation (LDA) in the framework of the Linearized Muffin-Tin-Orbitals (LMTO) method. The classical example of the doped Mott-insulator La_{1-x}Sr_xTiO_3 was studied by the new method and the results showed qualitative improvement in agreement with experimental photoemission spectra.Comment: 11 pages, 3 Postscript figures, LaTeX, submit in Journal of Physics: Condensed Matte

Mapping the Neural Substrates of Recent and Remote Visual Imprinting Memory in the Chick Brain

Social attachment formed by filial imprinting in newborn chicks undergoes a process of memory consolidation that involves rearrangement of its neural storage substrates. In the first 3 h after imprinting it depends on the integrity of the intermediate medial mesopallium (IMM) and beyond that time on unidentified memory storage structures dubbed S’. To search for the S’ memory system in the chick brain, we mapped and compared patterns of activity induced by retrieval of filial attachment memory before and after this critical transition. Chicks were trained in the visual imprinting task, and their memory was reactivated by imprinting stimulus either 1 h (recent memory retrieval) or 24 h (remote memory retrieval) after the completion of training. Patterns of brain activity were mapped by in situ hybridization to mRNA of an immediate early gene c-fos. We also mapped c-fos expression induced by the first presentation of the imprinting stimulus. Memory retrieval triggered massive c-fos expression in the chick brain both 1 and 24 h after the end of training. These activity patterns mostly coincided with the c-fos expression induced by the first presentation of imprinting stimulus. However, in the hippocampus c-fos induction was observed only after the first exposure to imprinting stimulus but not after memory retrieval. In the IMM, medio-rostral nidopallium/mesopallium, and hyperpallium densocellulare c-fos activation was induced by retrieval of only the remote but not of the recent memory. These c-fos mapping data point to the candidate brain structures for systems reorganization of imprinting memory in chicks

The nature of the ferromagnetic ground state in the Mn4 molecular magnet

Using ab initio band structure and model calculations we studied magnetic properties of one of the Mn$_4$ molecular magnets (Mn4(hmp)6), where two types of the Mn ions exist: Mn3+ and Mn2+. The direct calculation of the exchange constants in the GGA+U approximation shows that in contrast to a common belief the strongest exchange coupling is not between two Mn3+ ions (J_{bb}), but along two out of four exchange paths connecting Mn3+ and Mn2+ ions (J_{wb}). The microscopic analysis performed within the perturbation theory allowed to establish the mechanism for this largest ferromagnetic exchange constant. The charge ordering of the Mn ions results in the situation when the energy of the excited state in the exchange process is defined not by the large on-site Coulomb repulsion U, but by much smaller energy V, which stabilizes the charge ordered state. Together with strong Hund's rule coupling and specific orbital order this leads to a large ferromagnetic exchange interaction for two out of four Mn2+ --Mn3+ pairs.Comment: 12 pages, 10 figure

Changes in the population distribution and transport network of Saint Petersburg

The authors explores the interdependence between demographic changes and transport network centrality, using Saint Petersburg as an example. The article describes the demographic data for the period 2002-2015 and the transportation network data of 2006. The authors employ several methods of demographic research; they identified the centre of gravity of the population, produce the standard deviational ellipsis and use the kernel density estimation. The street network centrality of Saint Petersburg was analyzed using the Multiple Centrality Assessment Model (MCA) and the Urban Network Analysis Tool for ArcGIS. The analysis of the population distribution in Saint Petersburg shows that each area of the city has seen their population grow over the last thirteen years. However, it is the population of suburban areas that increased the most. The core area of the city has the tendency of outward diffusion, and the population gravity centre has been moving northwards. Spatial characteristics of the population growth, changes in the population gravity centre, the standard deviational ellipse and characteristics of the street network centrality show that Saint Petersburg is at the final stage of urbanization and its development pattern is similar to that of other major cities