Forbidden ordinal patterns in higher dimensional dynamics

Forbidden ordinal patterns are ordinal patterns (or rank blocks) that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L₀, it has forbidden patterns of any length L≥L₀ and their number grows superexponentially with L. Using recent results on topological permutation entropy, in this paper we study the existence and some basic properties of forbidden ordinal patterns for self-maps on n-dimensional intervals. Our most applicable conclusion is that expansive interval maps with finite topological entropy have necessarily forbidden patterns, although we conjecture that this is also the case under more general conditions. The theoretical results are nicely illustrated for n=2 both using the naive counting estimator for forbidden patterns and Chao’s estimator for the number of classes in a population. The robustness of forbidden ordinal patterns against observational white noise is also illustrated.     

Biaxial liquid-crystal elastomers: A lattice model

We present a simple coarse-grained lattice model for monodomain biaxial liquid-crystal elastomers and perform large-scale Monte Carlo simulations in the proposed model system. Orientational ordering --uniaxial or biaxial-- reflects in sample deformations on cooling the system. The simulation output is used to predict calorimetry data and deuterium magnetic resonance spectra.     

Modified Baptista type chaotic cryptosystem via matrix secret key

In 1998, M.S. Baptista proposed a chaotic cryptosystem using the ergodicity property of the simple low-dimensional and chaotic logistic equation. Since then, many cryptosystems based on Baptista's work have been proposed. However, over the years research has shown that this cryptosystem is predictable and vulnerable to attacks and is widely discussed. Among the weaknesses are the non-uniform distribution of ciphertexts and succumbing to the one-time pad attack (a type of chosen plaintext attack). In this Letter, our objective is to modify the chaotic cryptographic scheme proposed previously. We use a matrix secret key such that the cryptosystem would no longer succumb to the one-time pad attack.     

Chaotic secure communication based on strong tracking filtering

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate.     

On the effect of an applied magnetic field on the shear-induced pattern formation in nematic polymer liquid crystals

The effect of an applied magnetic field and of the boundaries on the stability of the shear flow of nematic polymer liquid crystals of the tumbling type with respect to the formation of the transient spatially periodic patterns that appears after the start-up of shearing is studied. The unidirectional shear of a nematic director initially uniformly oriented orthogonally to the sample plane and with strong anchoring is considered. The magnetic field is applied orthogonally to the sample plane or in the same direction of the flow. For a given value of the Ericksen number of the flow a critical value of the magnetic-to-viscous energy ratio shows up above which the uniform flow is stable. When the influence of the boundaries may be neglected, an internal Ericksen number that stays constant in a given material is considered such that the wavelength of the periodic pattern is a self-adjusted length. An internal generalized Ericksen number is defined such that it is a universal function of the magnetic-to-viscous energy ratio.To the memory of my mother     

Cryptanalysis of a chaos-based image encryption algorithm

A chaos-based image encryption algorithm was proposed in [Z.-H. Guan, F. Huang, W. Guan, Phys. Lett. A 346 (2005) 153]. In this Letter, we analyze the security weaknesses of the proposal. By applying chosen-plaintext and known-plaintext attacks, we show that all the secret parameters can be revealed.     

Analysis of Chemical Neutralization Products of Phosphonothiolates by Gas Chromatography Mass Spectrometry

A series of phosphonothiolates, including the highly toxic O-Ethyl-S-(2-diisopropylamino) ethyl methylphosphonothioate (VX), have been subjected to chemical neutralization reaction with metallic sodium. The phosphonothiolates decompose to their respective phosphonic and phosphonothioic acids and this results in the detoxification of VX. GC/MS technique in both EI and CI mode has been applied for reaction monitoring and final identification of the neutralization products formed in this reaction.     

Secure communication based on a four-wing chaotic system subject to disturbance inputs

In this paper, a two-input two-output secure communication scheme based on a four-wing four-dimensional chaotic system with disturbance inputs is discussed. Based on parameter modulation theory and Lyapunov stability theory, synchronization and secure communication between transmitter and receiver are achieved and two message signals are recovered via a convenient robust high-order sliding mode adaptative controller. In addition, the gains of the receiver system can be adjusted continually, the unknown parameters can be identified precisely and the disturbance inputs can be suppressed simultaneously by the proposed adaptative controller. Synchronization under the effect of noise is also considered. Computer simulations are done to verify the proposed methods and the numerical results show that the obtained theoretic results are feasible and efficient.     

External field-induced switching in nematic elastomers: A Monte Carlo study

We present a Monte Carlo study of external field-induced switching in nematic elastomers, employing a coarse-grained shearable lattice model. In large enough systems a full-wavelength Fréedericksz effect is observed --as opposed to the half-wavelength effect seen in ordinary nematics-- that clearly reflects in simulated polarized light textures, as well as in deuterium magnetic resonance spectra. The reorientation of mesogenic units is accompanied by pronounced shear deformations.     

Multidimensional Z-Matrix with Control Parameters and Its Applications in Image Encryption

An n-dimensional Z-matrix with control parameters is presented, and its periodicity and chaos are testified. Experimental results show that the proposed Z-matrix has a long period and changeable periodicity with different dimensions. Some examples of image encryption with a Z-matrix of different dimensions are listed for demonstrating its applications.