Control of fractional chaotic system based on fractional-order resistor—capacitor filter

We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional-order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.     

Periodic,quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β -FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.     

A chaotic hierarchical encryption/watermark embedding scheme for multi-medical images based on row–column confusion and closed-loop bi-directional diffusion

Security during remote transmission has been an important concern for researchers in recent years. In this paper, a hierarchical encryption multi-image encryption scheme for people with different security levels is designed, and a multi-image encryption(MIE) algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper. While ensuring secure communication of medical image information, people with different security levels have different levels of decryp...     

New chaotical image encryption algorithm based on Fisher–Yatess scrambling and DNA coding

Based on the Fisher–Yatess scrambling and DNA coding technology, a chaotical image encryption method is proposed. First, the SHA-3 algorithm is used to calculate the hash value of the initial password, which is used as the initial value of the chaotic system. Second, the chaotic sequence and Fisher–Yatess scrambling are used to scramble the plaintext,and a sorting scrambling algorithm is used for secondary scrambling. Then, the chaotic sequence and DNA coding rules are used to change the plaintext pixel values, which makes the ciphertext more random and resistant to attacks, and thus ensures that the encrypted ciphertext is more secure. Finally, we add plaintext statistics for pixel-level diffusion to ensure plaintext sensitivity. The experimental results and security analysis show that the new algorithm has a good encryption effect and speed, and can also resist common attacks.     

Extended AMAI-PCA technique based on multi-level Box–Behnken design

Previously, we reported a technique for in situ projection lens aberration measurement based on principal component analysis of aerial images (AMAI-PCA). The sampling approach of this technique has a great impact on the measurement range and accuracy. To meet the requirement of large aberration measurement, a multi-level Box–Behnken design approach is tested in conjunction with AMAI-PCA to build the aerial image space. Compared with regular Box–Behnken design, the new approach improves the accuracy by 30% when the amplitude of wavefront aberration is larger than 0.1λ.     

A new kind of nonlinear fractional-order chaotic phenomenon in coupled systems： coexistence of anti-phase and complete synchronization

In this paper, we have found a kind of interesting nonlinear phenomenon hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti- phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams Bashforth-Moulton algorithm. To support our theoretical analysis, simulation results are given.     

Performance comparison of Fabry–Perot and Mach–Zehnder interferometers for molecular Doppler lidar based on fringe-imaging technique

Fringe-imaging Fabry–Perot interferometer (FIFPI) and fringe-imaging Mach–Zehnder interferometer (FIMZI) used as frequency discriminator for incoherent molecular Doppler lidar were analyzed, respectively. For a pure molecular backscattered signal, performances (wind measurement sensitivity and signal-to-noise ratio) of both FIFPI and FIMZI systems were simulated based on the U.S. standard atmospheric model. Comparisons of two systems were made under the same emitting and receiving parameters with certain wind speed dynamic range. Simulated results show that, though relatively lower sensitivity to Doppler shift, the single-channel FIMZI system provides a factor of 1.3 times smaller error in the horizontal wind velocity than that of FIFPI at a range of 20 km. We expect that the FIMZI frequency discriminator would provide an effective technique to improve the measurement accuracy for incoherent molecular Doppler lidar.     

Copyright protection in digital museum based on digital holography and discrete wavelet transform

A new method to protect the copyright of digital museum based on digital holography is proposed.The Fresnel hologram of watermark image is embedded in the object to be protected through discrete wavelet transform(DWT).After the watermark detection,the copyright information appears in the reconstructed hologram.With the higher redundancy feature in the hologram,the proposed technique can actually survive several kinds of image processing.Experimental results prove that the presented method has good robustness in image protection.     

An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro–Macro decomposition

The concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 < ε ? 1, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields b and the simple extension to the case of a non-constant anisotropy intensity 1/ε. The mathematical approach and the numerical scheme are different from those presented in the previous work [P. Degond, F. Deluzet, A. Lozinski, J. Narski, C. Negulescu, Duality-based asymptotic-preserving method for highly anisotropic diffusion equations, Communications in Mathematical Sciences 10 (1) (2012) 1–31] and its considerable advantages are pointed out.     

Fourier–Mukai and Nahm transforms for holomorphic triples on elliptic curves

We define a Fourier–Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases, the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic equations on a triple—vortices—and explore some of its basic properties. Our approach combines direct methods with dimensional reduction techniques, relating triples over a curve with vector bundles over the product of the curve with the complex projective line.     

Absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations based on the perfectly matched layer technique

Absorbing boundary conditions for the nonlinear Euler and Navier–Stokes equations in three space dimensions are presented based on the perfectly matched layer (PML) technique. The derivation of equations follows a three-step method recently developed for the PML of linearized Euler equations. To increase the efficiency of the PML, a pseudo mean flow is introduced in the formulation of absorption equations. The proposed PML equations will absorb exponentially the difference between the nonlinear fluctuation and the prescribed pseudo mean flow. With the nonlinearity in flux vectors, the proposed nonlinear absorbing equations are not formally perfectly matched to the governing equations as their linear counter-parts are. However, numerical examples show satisfactory results. Furthermore, the nonlinear PML reduces automatically to the linear PML upon linearization about the pseudo mean flow. The validity and efficiency of proposed equations as absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations are demonstrated by numerical examples.     

Intense source of cold cesium atoms based on a two-dimensional magneto–optical trap with independent axial cooling and pushing

We report our studies on an intense source of cold cesium atoms based on a two-dimensional(2D) magneto–optical trap(MOT) with independent axial cooling and pushing.The new-designed source,proposed as 2D-HP MOT,uses hollow laser beams for axial cooling and a thin pushing laser beam to extract a cold atomic beam.With the independent pushing beam,the atomic flux can be substantially optimized.The total atomic flux maximum obtained in the 2D-HP MOT is4.02 × 1010atoms/s,increased by 60 percent compared to the traditional 2D+MOT in our experiment.Moreover,with the pushing power 10 μW and detuning 0Γ,the 2D-HP MOT can generate a rather intense atomic beam with the concomitant light shift suppressed by a factor of 20.The axial velocity distribution of the cold cesium beams centers at 6.8 m/s with an FMHW of about 2.8 m/s.The dependences of the atomic flux on the pushing power and detuning are studied in detail.The experimental results are in good agreement with the theoretical model.     

A new photopolymerizable holographic recording material based on acrylamide and N-hydroxymethyl acrylamide

new polyvinylalcohol-based photopolymeric holographic recording material has been developed. The recording is obtained by the copolymerization of acrylamide and N-hydroxymethyl acrylamide. Diffraction efficiencies near 50% are obtained with energetic exposure of 80mJ/cm². N-hydroxymethyl acrylamide can improve the optical quality of the film. With the increase of the concentration of N-hydroxymethyl acrylamide, the flatness of the film increases, scattering reduces and the straight image is clearer with a small distortion. The postexposure effect on the grating is also studied. The diffraction efficiency of grating increases further during postexposure, gradient of monomer exists after exposure.     

A convergence study of a new partitioned fluid–structure interaction algorithm based on fictitious mass and damping

We develop, analyze and validate a new method for simulating fluid–structure interactions (FSIs), which is based on fictitious mass and fictitious damping in the structure equation. We employ a partitioned method for the fluid and structure motions in conjunction with sub-iteration and Aitken relaxation. In particular, the use of such fictitious parameters requires sub-iterations in order to reduce the induced error in addition to the local temporal truncation error. To this end, proper levels of tolerance for terminating the sub-iteration procedure have been obtained in order to recover the formal order of temporal accuracy. For the coupled FSI problem, these fictitious terms have a significant effect, leading to better convergence rate and hence substantially smaller number of sub-iterations. Through analysis we identify the proper range of these parameters, which we then verify by corresponding numerical tests. We implement the method in the context of spectral element discretization, which is more sensitive than low-order methods to numerical instabilities arising in the explicit FSI coupling. However, the method we present here is simple and general and hence applicable to FSI based on any other discretization. We demonstrate the effectiveness of the method in applications involving 2D vortex-induced vibrations (VIV) and in 3D flexible arteries with structural density close to blood density. We also present 3D results for a patient-specific aneurysmal flow under pulsatile flow conditions examining, in particular, the sensitivity of the results on different values of the fictitious parameters.     

Human detection based on motion object extraction and head–shoulder feature

Aimed at the shortcomings of the traditional video monitoring system, human detection method in intelligent video monitoring system was researched. This paper proposed a human detection method based on motion object extraction and head–shoulder feature to complete human detection and statistics in video image sequences. Firstly, background subtraction based on adaptive threshold was used to extract foreground moving object information, then image erosion and image dilation were used to bypass the object shade and remove false object in order to optimize the results of motion object extraction. And finally, for realizing human moving object detection, we proposed the object discrimination algorithm based on human head–shoulder feature to complete human detection and statistics. Experimental results show that the method can successfully realize human detection and statistics. The method is highly accurate and has good real-time and extensive applications. The identification rate is 86% through human video sequences to test. This method can detect human automatically and provide the theoretical and technological base for object detection in the intelligent surveillance system.     

The WDM–ROF–PON based on linearly-polarization dual-wavelength fiber laser and CSRZ–DPSK modulation

In this paper, we design a linearly-polarized dual-wavelength fiber laser used in WDM–ROF–PON, which can achieve wire-line and wireless access synchronously. With polarization multiplexing, the dual-wavelength fiber laser is the union light source of WDM–PON. With the CSRZ–DPSK modulation, the wireless access system of ONU can save RF source and the frequency of radio carrier can be controlled by OLT. The networking has the credible transmission property, including fiber transmission and wireless access.     

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.     

Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials

Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which are deformations of those for the Wilson and Askey–Wilson polynomials in terms of a degree ?   (?=1,2,…$?=1,2,\dots$) eigenpolynomial. These polynomials are exceptional in the sense that they start from degree ??1$??1$ and thus not constrained by any generalisation of Bochner's theorem.