An Image Encryption Algorithm Based on a New Hybrid Power Exponent Chaotic System

Aiming at the problem of a small parameter value range when a one-dimensional chaotic system presents a chaotic state, this paper proposes a new type of hybrid power exponential chaotic system (HPECS). HPECS combines the classic one-dimensional Sine chaotic system to form a new chaotic system (HPECS-SS). Experiments show that the obtained new chaotic system has better chaotic performance, a more extensive parameter value range, and higher sensitivity. Simultaneously, on the basis of HPECS-SS, a new image encryption algorithm is proposed. The algorithm uses the key generated by the SHA-512 algorithm and HPECS-SS to iteratively output the chaotic sequence, SFY algorithm combines the chaotic sequence to perform two rounds of scrambling on the plaintext sequence to obtain the scrambling sequence, and finally, through the modulus operation to diffuse the scrambling sequence to form the encryption matrix of the plaintext image, simulation experiment analysis shows that the algorithm has a large key space, good encryption effect, and security; the pixel change rate (NPCR) and the normalized average change intensity (UACI) are close to ideal values which can resist various cryptanalysis and attacks.

Comparative Study of the Near-Surface Typhoon Wind Profile Fitting between Offshore and Onshore Areas

The study of typhoon wind profiles, especially offshore typhoon wind profiles, has been constrained by the scarcity of observational data. In this study, the Doppler wind lidar was used to observe the offshore wind profiles during Super Typhoon Mangkhut and onshore wind profiles during Super Typhoon Lekima. Four wind profile models, including the power law, logarithmic law, Deaves–Harris (D-H), and Gryning, were selected in the height range of 0–300 m to fit the wind profile. The variations in the power exponent with the mean wind speed and roughness length were also analyzed. The results showed that the wind profiles fitted by the four models were generally in good agreement with the observed wind profiles with correlation coefficients greater than 0.98 and root mean square deviations less than 0.5 m s−1. For the offshore case, the fitting degree of all wind profile models improved with increasing mean wind speed. Specifically, the D-H model had the highest fitting degree when the horizontal mean wind speed at 40 m was in the range of 8–25 m s−1, while the log-law model had the highest fitting degree when the wind speed exceeded 30 m s−1. For the onshore case, the fitting degree of the four wind profile models deteriorated with increasing mean wind speed, and the log-law model had the highest fitting degree in all wind speed intervals from 8 to 30 m s−1. For both offshore and onshore cases, the power exponent was less affected by mean wind speed and increased with increasing roughness length, and the logarithmic empirical model proposed in this study could well characterize the relationship between the power exponent and roughness length.

Generation and Propagation of Partially Coherent Power-Exponent-Phase Vortex Beam

We report on a partially coherent power-exponent-phase vortex beam (PC-PEPV), whose spatial coherence is controllable and the initial phase exhibits a periodic power exponential change. The PC-PEPV beam was generated experimentally with various spatial coherence widths, and its propagation properties were studied both numerically and experimentally. By modulating the topological charge (TC) and power order of the PC-PEPV beam, the structure of the vortex beam can be adjusted from circular to elliptic, triangular, quadrangle, and pentagon. When the power order is odd, the PC-PEPV beam with a negative TC can be generated, and the profiles of the PC-PEPV beam can be precisely controlled via adjusting the value of the power order. For the case of high spatial coherence width, the number of the dark cores in the polygonal intensity array of the PC-PEPV beam equals the magnitude of the TC. However, when decreasing the spatial coherence width, the dark cores vanish and the intensity gradually transforms into a polygonal light spot. Fortunately, from the modulus and phase distributions of the cross-spectral density (CSD), both the magnitude and sign of the TC can be determined. In the experiment, the modulus and phase distribution of the CSD are verified by the phase perturbation method. This study has potential applications in beam shaping, micro-particle trapping, and optical tweezers.

Hydrogel sphere impact cratering, spreading and bouncing on granular media

The impact of a hydrogel sphere onto a granular target results in both the deformation of the sphere and the formation of a prominent topographic feature known as an impact crater on the granular surface. We investigate the crater formation and scaling, together with the spreading diameter and post-impact dynamics of spheres by performing a series of experiments, varying the Young's modulus $Y$ and impact speed $U_{0}$ of the hydrogel spheres, and the packing fraction and grain size of the granular target. We determine how the crater diameter and depth depend on $Y$ and show the data to be consistent with those from earlier experiments using droplets and hard spheres. Most specifically, we find that the crater diameter data are consistent with a power law, where the power exponent changes more sharply when $Y$ becomes less than 200 Pa. Next, we introduce an estimate for the portion of the impact kinetic energy that is stored as elastic energy during impact, and thus correct the energy that remains available for crater formation. Subsequently, we determine the deformation of the hydrogel spheres and find that the normalized spreading diameter data are well collapsed introducing an equivalent velocity from an energy balance of the initial kinetic energy against surface and elastic energy. Finally, we observe that under certain intermediate values for the Young's modulus and impact velocities, the particles rebound from the impact crater. We determine the phase diagram and explain our findings from a comparison of the elastocapillary spreading time and the impact duration.

A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells

In this article, we explore a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells. The multi-directional FG material uses a power law rule with three power exponent indexes concerning three parametric coordinates. Nanoshell's geometries include the square plate, cylindrical and spherical panels with the side length considered in a nanoscale. Because 3D-IGA utilizes an approximation of NURBS basic functions to integrate from geometry modeling to discretized domain, it is the best promising candidate to fulfill a higher-order derivative requirement of the nonlocal theory on nanoshells. The numerical solutions are verified by those published in several pieces of literature to determine the current approach's accuracy and reliability. After a convergence solution is examined, a quartic NURBS basic function can yield ultra-converged and high-accurate results with a low computational cost. The findings show the size effect parameters which significantly impact the frequencies and the critical buckling factors of the multi-directional FG nanoshells. Generally, increases in the size effect parameters will cause declines in the frequencies and the critical buckling factors of the nanoshells.