Study of the electronic structure of Al(III) and Zn(II) complexes with organic ligands by quantum chemistry and photoelectron spectroscopy methods

Photoelectron spectra of aluminum complexes with 8-oxyquinoline (Alq ₃) and zinc complexes with N, N′-(o-phenylene)-bis(salicylidenediamine) (ZnSaloph) were measured on a photoelectron spectroscopy station at the Kurchatov Centre for Synchrotronic Radiation over the range of photon energies from 10 to 100 eV. Thin films of these compounds (∼20 nm thick) prepared by thermal evaporation onto glass substrates covered with transparent electroconductive layer of solid solution of tin and indium oxides (In₂O₃, SnO₂, ITO) were used as the objects of this study. The spectra of the valence band of these compounds and Al 2p level were measured. The data of quantum chemical calculations of the electronic structure obtained by the density functional theory are in good agreement with the experimental photoelectron spectra. Analysis of performance efficiency of the device was carried out on the basis of the results of calculation. This procedure does not result in decomposition of samples in the process of investigation and may be used for studying the electronic structure of coordination compounds with organic ligands in films.     

Minimal integer automaton behind crystal plasticity

Power law fluctuations and scale-free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova-type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study, and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer-valued automaton revealing inherent discreteness of the plastic flow.     

Multi-tiling and Riesz bases

Let S   be a bounded, Riemann measurable set in R^d${\mathbb{R}}^d$, and Λ be a lattice. By a theorem of Fuglede, if S   tiles R^d${\mathbb{R}}^d$ with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles  R^d${\mathbb{R}}^d$ with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer?s quasicrystals.     

Weak variations of Lipschitz graphs and stability of phase boundaries

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.     

Generalized Stationary Processes: Applications and Examples

We introduce and investigate special classes of generalized stationary processes: white-noise-type processes and power-low processes. Operators which generate white-noise-type processes are interesting, in particular, because of their importance to random matrix theory, triangular factorization of operators and spectral theory.     

Autocorrelation low coherence interferometry

This paper describes the development of a new modality of optical low coherence interferometry (LCI) that is called autocorrelation LCI (ALCI). The ALCI system employs a Michelson interferometer to measure longitudinal autocorrelation properties of the sample optical field and does not require a reference beam. As the result, there is no restrictions applied on the distance between the sample and the ALCI system, moreover, this distance can even change during the measurements. We report experiments using a proof-of-principle ALCI system on a multilayer phantom consisting of three surfaces defining two regions of different refractive indices. The experimental data are in excellent agreement with the predictions of the theoretical model.