Inverse Problems in Turbulent Dynamics of Light

The differential equations underlying the non-linear dynamics of turbulent fluid flow are extended to the transport of optical energy and optical phase in coherent lasers in a new theoretical framework. Since light acts like a pure, incompressible, inviscid fluid, the momentum and mass transport of the NavierStokes equations translate directly to the intensity and phase transport equations in scalar diffraction theory, respectively. The non-linear term in the phase transport equation describes the emergence of turbulent dynamics near cusps and singularities in the optical field, enabling insights into the topology and dynamics of turbulence/speckle in 6D phase space. A better understanding of the mathematical forms of turbulent wave dynamics allows for reformulating the inverse computational problem for the perennial and current problems in the physics and engineering - imaging through turbulent media, understanding stochastic effects in sub 20nm extreme ultraviolet lithography for extending Moore’s law, holographic reconstruction of chaotic diffusion in image processing - but in context of latest computational and sensing capabilities. Turbulence in visible laser light can be easily measured with inexpensive table-top laser sources, scientific cameras, and simple imaging optics, enabling volumetric energy measurements. Combined with the most current mathematical understanding and computational tools for hydrodynamics modeling, we hope to usher in a new understanding of super-linear dynamics in natural flow processes

The stationary points of the hierarchical three-body problem

ABSTRACT We study the stationary points of the hierarchical three body problem in the planetary limit (m1, m2 ≪ m0) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal stationary points of the quadrupole solution in the limit of small outer eccentricity e2 but that new families of stable fixed points occur in both prograde and retrograde cases. The most important new equilibria are those that branch off from the quadrupolar solutions and extend to large e2. The apsidal alignment of these families is a function of mass and inner planet eccentricity, and is determined by the relative directions of precession of ω1 and ω2 at the quadrupole level. These new equilibria are also the most resilient to the destabilizing effects of relativistic precession. We find additional equilibria that enable libration of the inner planet argument of pericentre in the limit of radial orbits and recover the non-linear analogue of the Laplace–Lagrange solutions in the coplanar limit. Finally, we show that the chaotic diffusion and orbital flips identified with the eccentric Kozai–Lidov mechanism and its variants can be understood in terms of the stationary points discussed here.

A Bijective Image Encryption System Based on Hybrid Chaotic Map Diffusion and DNA Confusion

Modern multimedia communications technology requirements have raised security standards, which allows for enormous development in security standards. This article presents an innovative symmetric cryptosystem that depends on the hybrid chaotic Lorenz diffusion stage and DNA confusion stage. It involves two identical encryption and decryption algorithms, which simplifies the implementation of transmitting and receiving schemes of images securely as a bijective system. Both schemes utilize two distinctive non-consecutive chaotic diffusion stages and one DNA scrambling stage in between. The generation of the coded secret bit stream employs a hybrid chaotic system, which is employed to encrypt or decrypt the transmitted image and is utilized in the diffusion process to dissipate the redundancy in the original transmitted image statistics. The transmitted image is divided into eight scrambled matrices according to the position of the pixel in every splitting matrix. Each binary matrix is converted using a different conversion rule in the Watson–Crick rules. The DNA confusion stage is applied to increase the complexity of the correlation between the transmitted image and the utilized key. These stages allow the proposed image encryption scheme to be more robust against chosen/known plaintext attacks, differential attacks, cipher image attacks, and information entropy. The system was revealed to be more sensitive against minimal change in the generated secret key. The analysis proves that the system has superior statistical properties, bulkier key space, better plain text sensitivity, and improved key sensitivity compared with former schemes.