scholarly journals MIXING IN COASTAL AREAS INFERRED FROM LYAPUNOV EXPONENTS: IMPLICATIONS FOR TRANSPORT

2012 ◽  
Vol 1 (33) ◽  
pp. 8
Author(s):  
Alejandro Orfila ◽  
Alvaro Galan ◽  
Gonzalo Simarro ◽  
Juan Manuel Sayol
Keyword(s):  
Lyapunov Exponents ◽  
Coherent Structures ◽  
Finite Size ◽  
Current Field ◽  
High Resolution Data ◽  
Finite Time Lyapunov Exponents ◽  
Lagrangian Drifters ◽  
Waves And Currents ◽  
Surface Mixing ◽  
And Diffusion

We study the horizontal surface mixing and the transport induced by waves, using local Lyapunov exponents and high resolution data from numerical simulations of waves and currents. By choosing the proper spatial (temporal) parameters we compute the Finite Size and Finite Time Lyapunov exponents (FSLE and FTLE) focussing on the local stirring and diffusion inferred from the Lagrangian Coherent Structures (LCS). The methodology is tested by deploying a set of eight lagrangian drifters and studying the path followed against LCS derived under current field and waves and currents.

scholarly journals Surface Ocean Mixing Inferred from Different Multisatellite Altimetry Measurements

2010 ◽  
Vol 40 (11) ◽  
pp. 2466-2480 ◽  
Author(s):  
Francisco J. Beron-Vera ◽  
María J. Olascoaga ◽  
Gustavo J. Goni
Keyword(s):  
Lyapunov Exponents ◽  
Coherent Structures ◽  
Diagnostic Tool ◽  
Turbulent Mixing ◽  
Finite Time ◽  
The Other ◽  
Sea Surface ◽  
Anomaly Field ◽  
Finite Time Lyapunov Exponents ◽  
Surface Ocean

Abstract Two sea surface height (SSH) anomaly fields distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) Altimetry are evaluated in terms of the effects that they produce on mixing. One SSH anomaly field, tagged REF, is constructed using measurements made by two satellite altimeters; the other SSH anomaly field, tagged UPD, is constructed using measurements made by up to four satellite altimeters. Advection is supplied by surface geostrophic currents derived from the total SSH fields resulting from the addition of these SSH anomaly fields to a mean SSH field. Emphasis is placed on the extraction from the currents of Lagrangian coherent structures (LCSs), which, acting as skeletons for patterns formed by passively advected tracers, entirely control mixing. The diagnostic tool employed to detect LCSs is provided by the computation of finite-time Lyapunov exponents. It is found that currents inferred using UPD SSH anomalies support mixing with characteristics similar to those of mixing produced by currents inferred using REF SSH anomalies. This result mainly follows from the fact that, being more easily characterized as chaotic than turbulent, mixing as sustained by currents derived using UPD SSH anomalies is quite insensitive to spatiotemporal truncations of the advection field.

scholarly journals Hyperchaotic Image Encryption Based on Multiple Bit Permutation and Diffusion

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 510
Author(s):  
Taiyong Li ◽  
Duzhong Zhang
Keyword(s):  
Big Data ◽  
Lyapunov Exponents ◽  
Image Encryption ◽  
Hyperchaotic System ◽  
Encryption Scheme ◽  
Image Content ◽  
Image Security ◽  
Level Data ◽  
Different Types ◽  
And Diffusion

Image security is a hot topic in the era of Internet and big data. Hyperchaotic image encryption, which can effectively prevent unauthorized users from accessing image content, has become more and more popular in the community of image security. In general, such approaches conduct encryption on pixel-level, bit-level, DNA-level data or their combinations, lacking diversity of processed data levels and limiting security. This paper proposes a novel hyperchaotic image encryption scheme via multiple bit permutation and diffusion, namely MBPD, to cope with this issue. Specifically, a four-dimensional hyperchaotic system with three positive Lyapunov exponents is firstly proposed. Second, a hyperchaotic sequence is generated from the proposed hyperchaotic system for consequent encryption operations. Third, multiple bit permutation and diffusion (permutation and/or diffusion can be conducted with 1–8 or more bits) determined by the hyperchaotic sequence is designed. Finally, the proposed MBPD is applied to image encryption. We conduct extensive experiments on a couple of public test images to validate the proposed MBPD. The results verify that the MBPD can effectively resist different types of attacks and has better performance than the compared popular encryption methods.

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