Nanoscopy of pairs of atoms by fluorescence in a magnetic field

Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. The relevant schemes are considered that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system

Signum Function Method for Generation of Correlated Dichotomic Chains

We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated from the Fourier transform of a binary correlator. The goal of our study is to reveal conditions under which one can construct binary sequences with a given pair correlator. Our results can be used in the construction of superlattices and waveguides with selective transport properties.Comment: 14 pages, 7 figure

Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

Revealing Network Connectivity From Dynamics

We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring the phase differences and the collective frequency reveals information about how the oscillators are interconnected. Sufficiently many repetitions for different driving conditions yield the entire network connectivity from measuring the dynamics only. For sparsely connected networks we obtain good predictions of the actual connectivity even for formally under-determined problems.Comment: 10 pages, 4 figure

Application of Supercomputer Technologies for Simulation of Socio-Economic Systems

To date, an extensive experience has been accumulated in investigation of problems related to quality, assessment of management systems, modeling of economic system sustainability. The studies performed have created a basis for formation of a new research area — Economics of Quality. Its tools allow to use opportunities of model simulation for construction of the mathematical models adequately reflecting the role of quality in natural, technical, social regularities of functioning of the complex socioeconomic systems. Extensive application and development of models, and also system modeling with use of supercomputer technologies, on our deep belief, will bring the conducted researches of social and economic systems to essentially new level. Moreover, the current scientific research makes a significant contribution to model simulation of multi-agent social systems and that isn’t less important, it belongs to the priority areas in development of science and technology in our country. This article is devoted to the questions of supercomputer technologies application in public sciences, first of all, — regarding technical realization of the large-scale agent-focused models (AFM). The essence of this tool is that owing to increase in power of computers it became possible to describe the behavior of many separate fragments of a difficult system, as social and economic systems represent. The article also deals with the experience of foreign scientists and practicians in launching the AFM on supercomputers, and also the example of AFM developed in CEMI RAS, stages and methods of effective calculating kernel display of multi-agent system on architecture of a modern supercomputer will be analyzed. The experiments on the basis of model simulation on forecasting the population of St. Petersburg according to three scenarios as one of the major factors influencing the development of social and economic system and quality of life of the population are presented in the conclusion