Vortex-induced vibrations (VIV) need to be accounted for in the design of marine structures such as risers and umbilicals. If a resonance state of the slender structure develops due to its interaction with the surrounding fluid flow, the consequences can be severe resulting in the accelerated fatigue and structural damage. Wake oscillator models allow to estimate the fluid force acting on the s...

Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alter...

This paper proposes a procedure for the parameter identification of Tamura’s wake-oscillator model. A multiple timescale analysis dimensionless model shows that response is governed by two groups D0 and D1, highlighting importance forcing terms in governing equations, total (aerodynamic structural) damping coefficient ? fluid Van der Pol oscillator. In particular, this approach provides simple ...

Mathematical modeling has played a significant role in building our understanding of sleep-wake and circadian behavior. Over the past 40 years, phenomenological models, including the two-process model and oscillator models, helped frame experimental results and guide progress in understanding the interaction of homeostatic and circadian influences on sleep and understanding the generation of ra...

We propose a reduced-order model for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its ...