Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV ₁ ,...,V _r in a toric varietyP and the system of differential operators annihilating the special generalized hypergeometric series ⁰ constructed from the fan . Using this generalized hypergeometric series, we propose conjectural mirrorsV ofV and the canonicalq-coordinates on the moduli spaces of Calabi-Yau manifolds.In the second part of the paper we consider some examples of Calabi-Yau 3-folds having Picard number >1 in products of projective spaces. For conjectural mirrors, using the recurrent relation among coefficients of the restriction of the hypergeometric function ⁰ on a special line in the moduli space, we determine the Picard-Fuchs equation satisfied by periods of this special one-parameter subfamily. This allows to obtain some sequences of integers which can be conjecturally interpreted in terms of Gromov-Witten invariants. Using standard techniques from enumerative geometry, first terms of these sequence of integers are checked to coincide with numbers of rational curves on Calabi-Yau 3-folds.     

Step structures on III-V phosphide (001) surfaces: how do steps and Sb affect CuPt ordering of GaInP2?

The observation of III-V phosphide (001)-(2 x 2) surfaces makes it possible to solve a long standing mystery of step structures. First-principles calculations show that a bulklike type-B step on a hydrogenated 2 x 2 surface is more stable than a rebonded one by 1.1 eV/unit step. In contrast, this energy difference for a H-free beta(2 x 4) surface is only 0.5 eV/unit step. The large difference explains why the CuPt ordering of GaInP is stronger in metal-organic chemical vapor deposition than in molecular beam epitaxy. However, a minute amount of Sb will preferentially attach to the 2 x 2 surface steps and induce additional step structures that cause ordering disruption.     

Growth model for atomic ordering: the case for quadruple-period ordering in GaAsSb alloys

Quadruple-period ordering in GaAsSb alloys is studied both theoretically and experimentally. A growth model is proposed to account for the observed three-dimensional (3D) ordered structure. The model is qualitatively different from the widely accepted surface reconstruction and dimerization-induced ordering models that strictly speaking explain only the in-plane 2D patterns. Here, we show that the already ordered substrate will affect the reconstruction of the growth front with respect to the substrate to ensure a correct stacking of the individual 2D ordered layers into the observed 3D lattice.     

Effect of IR illumination on photocurrent spectra in CdS crystals

Low-temperature near-band-edge photoconductivity (PC) spectra of CdS crystals were studied as a function of IR illumination intensity in the PC quenching interval. The photocurrent quenching by IR light of the PC response profile has been investigated. An analysis of these relationships permitted establishing a direct connection between the r photoconductivity centers and the near-band-edge structure of the spectrum. The effect of “pinning” of majoritycarrier lifetime on the semiconductor surface has been discovered and interpreted. It is proposed that surface-acceptor states in CdS crystals play the part of surface photoconductivity centers. Fiz. Tverd. Tela (St. Petersburg) 41, 1181–1184 (July 1999)     

Features of the excitonic optical reflection curves of GaAs crystals

The excitonic optical reflection curves are investigated for GaAs crystals subjected to a surface-sensitive electron bombardment. The observed features of the curves can be explained on a qualitative level by using an extremely simple square-well approximation of the subsurface excitonic potential. Fiz. Tverd. Tela (St. Petersburg) 39, 610–612 (April 1997)     

Mathematical models based on singular integral equations with non-Carleman shift. Analysis of solvability and numerical methods of solution

We consider some examples of systems whose functionality can be described with the help of mathematical models based on singular integral equations with non-Carleman shift. For this type of equations, we have obtained an estimate for the dimension of the kernel of the corresponding operator and proposed numerical methods for both evaluating the dimension of the kernel and constructing solutions.     

Reactions of water molecules in silica-based network glasses

Given that H(2)O dissolves minimally in quartz, the mechanism for the ubiquitous dissolution of H(2)O in silica glasses has been a long-standing puzzle. We report first-principles calculations in prototype silica glass networks and identify the ring topologies that allow the exothermic dissolution of H(2)O as geminate Si-O-H groups. The topological constraints of these reactions explain both the observed saturation of Si-O-H concentrations and the observed increase in the average Si-Si distance. In addition, calculations of H(2)O and Si-O-H dissociation account for the observed response to radiation by wet thermally grown SiO(2).