Abstract:
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be splitted into two parts: pseudo-continuous and strongly unstable. The pseudo-continuous part of the spectrum mediates destabilization of periodic solutions.

Sociocultural-interdeterminist dialogical
approach focuses attention on the caused interdeteministic character of mutual
relations of situational, personal and activity determinants of the behaviour,
staticized in concrete historical cultural context. For example, a change in a
situational context leads to changes both in the person, and in his or her
activity. Achievement of changes in the person and his or her activity assumes
creation of the special conditions promoting to their actualization, etc. For
understanding of the nature of progress in culture and science the theoretical
construct “cultural-scientific tradition” is offered, allowing to trace changes
in common cultural and scientific worldview throughout the human history.
Consideration of personality problems is carried out in a three-dimensional
continuum conscious-unconscious-existential, allowing to capture all variety of
displays of psychological phenomenology. Proceeding from understanding of
culture as orientational and normative structure of behaviour and as
communicative matrix by means of which the behaviour is interpreted,
integrated, coordinated and authorized (R. Priest), efficiency of use of the
conceptual device of the epistemic approach of Michel Foucault and cultural
framing of E. Goffman to understanding of intercultural interaction specificity
is proved. The epistemic differences of European (graphic), Chinese, and
classic Arabic languages are demonstrated. Intercultural competence is
considered in aspect of ability of formation of shared meanings and experiences
on the basis of mastering by knowledge about originalities of language, values
and norms, experiences and behavioral algorithms of each other. The basis of
such mutual understanding creates the dialogue that assumes unconditional
acceptance of another based on tolerance and pluralism, the joint extension of
the horizons directed on formation and development of coordinated and mutually
endured values and senses. As unit of the analysis of intercultural interaction
the evaluation of a sharedness of meanings and experiences is offered. Results
of empirical research of the given approach on the example of formation of
interpersonal mutual understanding of the Belarus and Chinese students are
presented.

Abstract:
We perform bifurcation analysis of plane wave solutions in one-dimensional cubic-quintic Ginzburg-Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is introduced. For intermediate values of the delay, bifurcation diagrams are obtained by a combination of analytical and numerical methods. For large delays, using an asymptotic approach we classify plane wave solutions into strongly unstable, weakly unstable, and stable. The results of analytical bifurcation analysis are in agreement with those obtained by direct numerical integration of the model equation.

Abstract:
Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability of synchronous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. This allows a universal classification of networks with respect to their synchronization properties and solves the problem of complete synchronization in networks with strongly delayed coupling.

Abstract:
We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state in a ring with a large number of nodes. Applying these results to unidirectionally coupled Duffing oscillators, we explain the phenomenon of a fast transition to chaos, which has been numerically observed in such systems. More specifically, the transition to chaos occurs on an interval of a generic control parameter that scales as the inverse square of the size of the ring, i.e. for sufficiently large system, we observe practically an immediate transition to chaos.

Abstract:
We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability of synchronous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. We give details of the proof of this structure and discuss the resulting universal classification of networks with respect to their synchronization properties. We illustrate this classification by means of several prototype network topologies.

Abstract:
We consider a general problem of laser pulse heating of spherical metal particles with the sizes ranging from nanometers to millimeters. We employ the exact Mie solutions of the diffraction problem and solve heat-transfer equations to determine the maximum temperature at the particle surface as a function of optical and thermometric parameters of the problem. The main attention is paid to the case when the thermometric conductivity of the particle is much larger than that of the environment, as it is in the case of metal particles in fluids. We show that in this case at any given finite duration of the laser pulse the maximum temperature rise as a function of the particle size reaches an absolute maximum at a certain finite size of the particle, and we suggest simple approximate analytical expressions for this dependence which covers the entire range of variations of the problem parameters and agree well with direct numerical simulations.

Abstract:
We analyze a metal-dielectric structure composed of a silicon nanoparticle coupled to a stack of split-ring resonators, and reveal the possibility of optically-induced antiferromagnetic response of such a hybrid meta-molecule with a staggered pattern of the induced magnetization. We show that a hybrid metamaterial created by a periodic lattice of the meta-molecules supports antiferromagnetic modes with a checker-board pattern and the propagation of spin waves, opening new ways for manipulating artificial antiferromagnetism at high frequencies with low-loss materials.

Abstract:
We investigate oscillation dynamics of a periodic structure of the $180^\circ$ domain walls in nanometricaly thin substrate-deposited ferroelectric films and superlattices. We calculate dynamic permittivity of such structures and reveal a collective resonance mode, which in the typical ferroelectric compounds, PbTiO3/SrTiO3, lies in the sub- and low THz frequency range of 0.3-3THz. We propose the reflection-absorbtion spectroscopy experiments to observe this mode.

Abstract:
High-refractive index dielectric nanoparticles may exhibit strong directional forward light scattering at visible and near-infrared wavelengths due to interference of simultaneously excited electric and magnetic dipole resonances. For a spherical high-index dielectric, the so-called first Kerker's condition can be realized, at which the backward scattering practically vanishes for some combination of refractive index and particle size. However, Kerker's condition for spherical particles is only possible at the tail of the scattering resonances, when the particle scatters light weakly. Here we demonstrate that significantly higher forward scattering can be realized if spheroidal particles are considered instead. For each value of refractive index exists an optimum shape of the particle, which produces minimum backscattering efficiency together with maximum forward scattering. This effect is achieved due to the overlapping of magnetic and electric dipole resonances of the spheroidal particle at the resonance frequency. It permits the design of very efficient, low-loss optical nanoantennas.