Hyperbolic diffusion in chaotic systems

We consider a deterministic process described by a discrete one-dimensional chaotic map and study its diffusive-like properties. Starting with the corresponding Frobenius-Perron equation we derive an approximate evolution equation for the probability distribution which is a partial differential equation of a hyperbolic type. Consequently, the process is correlated, non-Markovian, non-Gaussian and the information propagates with a finite velocity. This is in clear contrast to conventional diffusion processes described by a standard parabolic diffusion equation with an infinite velocity of information propagation. Our approach allows for a more complete characterisation of diffusion dynamics of deterministic systems.     

The dynamics of multidimensional cosmological models in the presence of quantum effects. I. The case FRW ×T D at high temperatures

The dynamical system approach is applied to the study of dynamics of multidimensional cosmological models with topology FRW ×T ^D (D-dimensional torus) in the presence of high-temperature quantum effects. The stability methods developed in the paper of Szydowski (Gen. Rel. Grav.,20, 221, 1988) are used in the analysis of typical states of the metric in the neighborhood of singularities and for large time values. The problems of dynamical dimensional reduction, structure of singularities, isotropization, etc., are discussed in this context.     

Determination of retained austenite in bearing steel

M?ssbauer effect experiments in scattering geometry were performed for gauging plates and bearings in order to measure the retained austenite content. The results, obtained from numerical calculations of Mössbauer spectra are compared with the X-ray diffraction measurements. A simple three point Mössbauer effect technique is applied in order to decrease the time of measurements in the industrial use.     

Identifying Particle Correlations in Quantum Hall Regime

We introduce a method that allows the disclosure of correlations between particle positions in an arbitrary many‐body system. The method is based on a well‐known simulated annealing algorithm and the proposed artificial distribution technique. Additionally, we investigate correlations in quantum Hall liquids (we consider many‐body wave functions that have been recently determined via the cyclotron subgroup model) and present three‐dimensional plots of configuration probability distributions that have been established from numerical simulations. We demonstrate that the preferred simultaneous positions of particles (configurations of positions, which correspond to large values of a system's probability distribution, ) tend to form complicated geometric structures, which are equivalent to classical Wigner crystals only for Laughlin states. Furthermore, we claim that quantum Hall liquids attributed to non‐Laughlin fillings are correlated on subdomains rather than on a whole particle domain (due to a quantizing magnetic field, which modifies the topology of a system's dynamics). Finally, we characterize Hall‐like internal orders in terms of statistical correlations (one‐dimensional unitary representations of cyclotron subgroups). Our conclusions concerning the stability of many‐body states agree with transport measurements and various numerical studies.     

Quantum Prisoner’s Dilemma game on hypergraph networks

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.     

Relaxation of excited states of Tm3+ and Tm3+-Eu3+ energy transfer in YVO4 crystal

Tm³⁺-Eu³⁺ energy transfer processes and relaxation dynamics of the ³ H ₄ and ³ F ₄ excited states of Tm³⁺ ions in 1 at. % Tm³⁺, 5 at. % Eu³⁺:YVO₄ single crystal were studied. Contribution of Tm³⁺-Eu³⁺ energy transfer reduces effectively the lifetime of terminal level in a potential ³ H ₄–³ F ₄ laser transition at around 1.48 μm. Adverse quenching of the ³ H ₄ emission by Eu³⁺ ions is found to be less efficient than that reported for Tm³⁺ + Tb³⁺ system in YVO₄. The classical Inokuti–Hirayama model accounts well for an experimental decay curve of the ³ H ₄ emission recorded for co-doped crystal. Stimulated emission cross section for ³ H ₄–³ F ₄ transition of Tm³⁺ at around 1.48 μm was analyzed taking into account the anisotropy of YVO₄ crystal. PACS 42.55.Xi; 42.62.Fi     

Pseudotwistors

We deal with the Hermitian Hurwitz pairs of signature (, s), + s = 5 + 4, | + 1 – s| = 2 + 4m;, m = 0, 1,.... We introduce the Hurwitz twistors for signature (3, 2) and its dual (1, 4) and we indicate the relationship between Hurwitz and Penrose twistors. The signatures (1, 8) and (7, 6) give rise to pseudotwistors and bitwistors, respectively. For pseudotwistors, we prove a counterpart of the Penrose theorem in the local version, on real analytic solutions of the related spinor equations versus harmonic forms, and in the semiglobal version, on holomorphic solutions of those equations versus Dolbeault cohomology groups. We prove an atomization theorem: There exist complex structures on isometric embeddings for the Hermitian Hurwitz pairs so that the embeddings are real parts of holomorphic mappings.     

Stereocontrolled Organocatalytic Strategy for the Synthesis of Optically Active 2,3‐Disubstituted cis‐2,3‐Dihydrobenzofurans

An intramolecular, organocatalyzed Michael addition has been developed to obtain biologically important 2,3‐disubstituted cis‐2,3‐dihydrobenzofurans. By using mandelic acid salts of primary aminocatalysts, derived from cinchona alkaloids, the intramolecular cyclization reaction has been developed to proceed in high yield, with moderate to good diastereoselectivity, and up to 99 % ee. Based on the absolute configuration of the formed 2,3‐disubstituted‐cis‐2,3‐dihydrobenzofurans and by considering the observed substrate scope restrictions, a mechanistic rationalization has been presented.