Silicon nitride (Si3N4) ceramics are used in numerous applications because of their superior mechanical properties. Their intrinsically brittle nature is a critical issue, but can be overcome by introducing whisker-like microstructural features. However, the formation of such anisotropic grains is very sensitive to the type of cations used as the sintering additives. Understanding the origin of dopant effects, central to the design of high-performance Si3N4 ceramics, has been sought for many years. Here we show direct images of dopant atoms (La) within the nanometre-scale intergranular amorphous films typically found at grain boundaries, using aberration corrected Z-contrast scanning transmission electron microscopy. It is clearly shown that the La atoms preferentially segregate to the amorphous/crystal interfaces. First-principles calculations confirm the strong preference of La for the crystalline surfaces, which is essential for forming elongated grains and a toughened microstructure. Whereas principles of micrometre-scale structural design are currently used to improve the mechanical properties of ceramics, this work represents a step towards the atomic-level structural engineering required for the next generation of ceramics.

Observation of rare-earth segregation in silicon nitride ceramics at subnanometre dimensions

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov–Arnold–Moser (KAM) theorem1,2,3,6,7,8,9—a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt2. By contrast, ‘non-KAM’ chaos switches on and off abruptly at critical values of the perturbation frequency6,7,8,9. This type of dynamics has wide-ranging implications in the theory of plasma physics10, tokamak fusion11, turbulence6,7,12, ion traps13, and quasicrystals6,8. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice22,23,24,25,26,27 with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns6,7,8,9,10,12,13,14,15,16 in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices

In this paper, the limit case of the SD (smooth and discontinuous) oscillator is studied. This system exhibits standard dynamics governed by the hyperbolic structure associated with the stationary state of the double-well. The substantial deviation from the standard dynamics is the non-smoothness of the velocity in crossing from one well to another, caused by the loss of local hyperbolicity due to the discontinuity. Without dissipation, the KAM structure on the Poincare section is constructed with generic KAM curves and a series of fixed points associated with surrounded islands of quasi-periodic orbits and the chaotic connection orbits. It is found that, for a fixed set of parameters, a special chaotic orbit exits there which fills a finite region and connects a series of islands dominated by different chains of fixed points. As one adds weak dissipation, the periodic solutions in this finite region remain unchanged while the quasi-periodic solutions (isolated islands) are converted to the corresponding periodic solutions. The relevant dynamics for the system with weak dissipation under external excitation is shown having period doubling bifurcation leading to chaos, and multi-stable solutions.

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The limit case response of the archetypal oscillator for smooth and discontinuous dynamics

Chaos-based stream ciphers form a prospective class of data encryption techniques. Usually, in chaos-based encryption schemes, the pseudo-random generators based on chaotic maps are used as a source of randomness. Despite the variety of proposed algorithms, nearly all of them possess many shortcomings. While sequences generated from single-parameter chaotic maps can be easily compromised using the phase space reconstruction method, the employment of multi-parametric maps requires a thorough analysis of the parameter space to establish the areas of chaotic behavior. This complicates the determination of the possible keys for the encryption scheme. Another problem is the degradation of chaotic dynamics in the implementation of the digital chaos generator with finite precision. To avoid the appearance of quasi-chaotic regimes, additional perturbations are usually introduced into the chaotic maps, making the generation scheme more complex and influencing the oscillations regime. In this study, we propose a novel technique utilizing the chaotic maps with adaptive symmetry to create chaos-based encryption schemes with larger parameter space. We compare pseudo-random generators based on the traditional Zaslavsky map and the new adaptive Zaslavsky web map through multi-parametric bifurcation analysis and investigate the parameter spaces of the maps. We explicitly show that pseudo-random sequences generated by the adaptive Zaslavsky map are random, have a weak correlation and possess a larger parameter space. We also present the technique of increasing the period of the chaotic sequence based on the variability of the symmetry coefficient. The speed analysis shows that the proposed encryption algorithm possesses a high encryption speed, being compatible with the best solutions in a field. The obtained results can improve the chaos-based cryptography and inspire further studies of chaotic maps as well as the synthesis of novel discrete models with desirable statistical properties.

Adaptive chaotic maps and their application to pseudo-random numbers generation

A natural-physical approach is pursued in uncovering basic timing and phase relations in human rhythmic movement. The approach is based on the theory of nonlinear oscillatory motion, entrained by continuously and discretely distrib- uted forcing. In the context of juggling three balls in a figure-eight pattern, a preliminary modeling attempt of the cyclical hand motion suggested that the dynamics underwriting juggling are captured best by a discretely kicked, highly nonlinear, self-sustained oscillator. Discretely kicked, nonlinear oscillators may be characterized by regime diagrams that depict the periodic (phase-locked) and quasiperiodic (not phase-locked) regimes in which the system can operate depending on the magnitude of the kicks. This article provides evidence for 2-quasiperiodicity and near, but not perfect, phase locking between tl/tf and tu/tf (where tl is the mean time that the hands move loaded with a ball, tu is the mean time that the hands move empty, and tf is the mean flight time of the b...

Timing and Phase Locking in Cascade Juggling

Particles within a stochastic—or chaotic—web in phase space can be accelerated to high energies even by weak magnetic fields, and the properties of the web show similarities to the quasicrystal state. Examples of webs with five- and sevenfold symmetries are given. The establishment of stochastic webs and structural coverings of the phase plane may yield new and unexpected results.

Minimal chaos and stochastic webs

Multidimensional Hamiltonian chaos

The experience obtained during the organization and operation of a system for the on-line reception, processing, and dissemination of satellite data covering the entire territory of Russia for the ...

Near real-time satellite monitoring of russia for forest fire protection

The authors outline how a decentralized ground reception and processing network for satellite remote sensing data has the potential to provide information more efficiently and rapidly than Russia's existing network of a few large central facilities that are charged with supplying preprocessed data to the user community. The components and linkages in the proposed new network are described.

M. Yu. Zakharov

Papers

Minimal chaos and stochastic webs

Multidimensional Hamiltonian chaos

Near real-time satellite monitoring of russia for forest fire protection

An alternative strategy for the development of a satellite data ground reception and processing network in russia