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In this paper, we examine the possible usage of compressive sampling (CS) for the efficient measurement and analysis of floating breakwaters dynamics. We model the dynamics of a box-type floating breakwater in a random sea environment with the Bretschneider-Mitsuyasu spectrum. The spectral method involving FFT and IFFT routines is used for the simulation and CS reconstruction purposes of the displacement and velocity parameters. The time series of forces are calculated using the Morison equation. It is also shown that those vibration parameters can be limited and suppressed to a certain degree by a tuned-mass-damper. The advantages of using the CS for the tuned-mass-damper-controlled vibration parameter measurement and analysis are also discussed. Our findings may provide convenience for the effective and efficient strategies for the vibration-induced problems of floating platforms including wave energy converters and offshore platforms.

• Rogue heat and diffusion waves are investigated in the frame of nonlinear heat equations. • It is shown that modulation instability triggers the formation rogue heat and diffusion waves. • Characteristics and statistics of rogue heat and diffusion waves are analyzed. In this paper, we numerically show and discuss the existence and characteristics of rogue heat and diffusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the generation of unexpected and large fluctuations in the frame of these models. These fluctuations can be named as rogue heat (diffusion) waves. We discuss the properties and statistics of such rogue waves. Our results can find many important applications in many branches such as the nonlinear heat transfer, turbulence, financial mathematics, chemical or biological diffusion, nuclear reactions, subsurface water infiltration, and pore water pressure diffusion modeled in the frame of nonlinear Terzaghi consolidation models, just to name a few. [ABSTRACT FROM AUTHOR]