Growth and Magnetooptical Properties of Anisotropic TbF3 Single Crystals

The present paper investigates the Faraday effect and absorption and luminescence spectra of single-crystal TbF3 measured at 90 K and 300 K. The optical-quality single-phase TbF3 crystals (structural type β-YF3) were grown by the Bridgman technique. Faraday rotation angles were measured at remagnetization along the [100] crystallographic axis. Low temperature optical measurements were carried out along the [100] axis. “Quasi-doublet” sublevels with energy at 0 cm-1, 65 cm-1 and 190 cm-1, and also a singlet sublevel with energy at 114 cm-1 located in the ground 7F6 multiplet were determined from the low temperature luminescence spectra. The Van-Vleck behavior of the magnetic susceptibility χb can be satisfactorily explained by the magnetic mixing of wave functions belonging to the ground and first excited “quasi-doublet” sublevels at 0 and 65 cm-1, respectively. Analysis of the oscillation dependences of the rotation angle showed that the value of the natural birefringence (Δn ≈ 0.0186) remains nearly constant within the wavelength and temperature ranges under investigation. As the temperature decreases, we find significant increases in the oscillation amplitude of the rotation angle and in the Verdet constant V. The spectral dependences V(χ) are linear throughout the temperature range. The magnetooptical activity of TbF3 can be explained by means of the spin- and parity-allowed electric-dipole 4f→5d transitions in the Tb3+ ions

The choice between delta and shift operators for low-precision data representation

Low-precision data types for embedded applications reduce the power consumption and enhance the price-performance ratio. Inconsistence between the specified accuracy of a designed filter or controller and an imprecise data type can be overcome using the δ-operator, an alternative to the traditional discrete-time z-operator. Though in many cases it significantly increases accuracy, sometimes it shows no advantage over the shift operator. So the problem of choice between delta and shift operator arises. Therefore, a study on δ-operator applicability bounds is needed to solve this problem and provide δ-operator efficient practical use. In this paper we introduce a concept of the δ-operator applicability criterion. The discrete system implementation technique with discrete-time operator choice is given for the low-precision machine arithmetic

Adaptive Chaotic Maps in Cryptography Applications

Chaotic cryptography is a promising area for the safe and fast transmission, processing, and storage of data. However, many developed chaos-based cryptographic primitives do not meet the size and composition of the keyspace and computational complexity. Another common problem of such algorithms is dynamic degradation caused by computer simulation with finite data representation and rounding of results of arithmetic operations. The known approaches to solving these problems are not universal, and it is difficult to extend them to many chaotic systems. This chapter describes discrete maps with adaptive symmetry, making it possible to overcome several disadvantages of existing chaos-based cryptographic algorithms simultaneously. The property of adaptive symmetry allows stretching, compressing, and rotating the phase space of such maps without significantly changing the bifurcation properties. Therefore, the synthesis of one-way piecewise functions based on adaptive maps with different symmetry coefficients supposes flexible control of the keyspace size and avoidance of dynamic degradation due to the embedded technique of perturbing the chaotic trajectory

Improving chaos-based pseudo-random generators in finite-precision arithmetic

One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined by the chaotic orbits. In this study, we show that the results obtained using such an approach are very prone to rounding errors and discretization effects. Thus, it appears that the generated sequences are close to random even when parameters correspond to non-chaotic oscillations. In this study, we confirm that the actual source of pseudo-random properties of bits in a binary representation of numbers can not be chaos, but computer simulation. We propose a technique for determining the maximum number of bits that can be used as the output of a pseudo-random sequence generator including chaos-based algorithms. The considered approach involves evaluating the difference of the binary representation of two points obtained by different numerical methods of the same order of accuracy. Experimental results show that such estimation can significantly increase the performance of the existing chaos-based generators. The obtained results can be used to reconsider and improve chaos-based cryptographic algorithms

Improving Chaotic Image Encryption Using Maps with Small Lyapunov Exponents

Chaos-based encryption is one of the promising cryptography techniques that can be used. Although chaos-based encryption provides excellent security, the finite precision of number representation in computers affects decryption accuracy negatively. In this paper, a way to mitigate some problems regarding finite precision is analyzed. We show that the use of maps with small Lyapunov exponents can improve the performance of chaotic encryption scheme, making it suitable for image encryption

Refinement of the Congruently Melting Composition of Nonstoichiometric Fluorite Crystals Ca1-xYxF2x (x = 0.01–0.14)

The concentration series of nonstoichiometric crystals Ca1–xYxF2+x (x = 0.01–0.14) was obtained from a melt by directional crystallization to refine the composition of the temperature maximum on the melting curves. A precision (±9 × 10−5 Å) determination of lattice parameters of the Ca1–xYxF2+x crystals with the structure of fluorite (sp. gr. Fm-3m) was performed, and a linear equation of their concentration dependence was calculated: a(x) = 5.46385(5) + 0.1999(4) x. The distribution of yttrium along the crystals Ca1–xYxF2+x, the content of which is determined by the precision lattice parameters, is studied. The congruently melting composition x = 0.105(5) of the Ca1–xYxF2+x phase is refined by the method of directional crystallization

Study of two-memcapacitor circuit model with semi-explicit ODE solver

This article discusses software tools for studying non-linear dynamical systems. For a detailed analysis of the behavior of chaotic systems stepsize-parameter diagrams are introduced. A new self-adjoint semi-explicit algorithm for the numerical integration of differential equations is described. Two modifications of the proposed method are represented. A two-memcapacitor circuit is selected as a test dynamical system. Symmetry, accuracy and performance analysis of semi-explicit extrapolation ODE solver are considered in a series of computational experiments. Phase space of the two-memcapacitor circuit model, stepsize-parameter diagrams and dynamical maps are given as experimental findings

Adaptive Chaotic Maps in Cryptography Applications

Chaotic cryptography is a promising area for the safe and fast transmission, processing, and storage of data. However, many developed chaos-based cryptographic primitives do not meet the size and composition of the keyspace and computational complexity. Another common problem of such algorithms is dynamic degradation caused by computer simulation with finite data representation and rounding of results of arithmetic operations. The known approaches to solving these problems are not universal, and it is difficult to extend them to many chaotic systems. This chapter describes discrete maps with adaptive symmetry, making it possible to overcome several disadvantages of existing chaos-based cryptographic algorithms simultaneously. The property of adaptive symmetry allows stretching, compressing, and rotating the phase space of such maps without significantly changing the bifurcation properties. Therefore, the synthesis of one-way piecewise functions based on adaptive maps with different symmetry coefficients supposes flexible control of the keyspace size and avoidance of dynamic degradation due to the embedded technique of perturbing the chaotic trajectory

Adaptive Chaotic Maps in Cryptography Applications

Chaotic cryptography is a promising area for the safe and fast transmission, processing, and storage of data. However, many developed chaos-based cryptographic primitives do not meet the size and composition of the keyspace and computational complexity. Another common problem of such algorithms is dynamic degradation caused by computer simulation with finite data representation and rounding of results of arithmetic operations. The known approaches to solving these problems are not universal, and it is difficult to extend them to many chaotic systems. This chapter describes discrete maps with adaptive symmetry, making it possible to overcome several disadvantages of existing chaos-based cryptographic algorithms simultaneously. The property of adaptive symmetry allows stretching, compressing, and rotating the phase space of such maps without significantly changing the bifurcation properties. Therefore, the synthesis of one-way piecewise functions based on adaptive maps with different symmetry coefficients supposes flexible control of the keyspace size and avoidance of dynamic degradation due to the embedded technique of perturbing the chaotic trajectory