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Parametric rolling is a parametric excitation phenomenon caused by GM variation in waves. There are a lot of studies of the estimation the conditions, the occurrence, and the amplitude of parametric rolling. On the other hand, there are…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear…
Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
Parametric rolling is one of the dangerous dynamic phenomena. In order to discuss the safety of a vessel when a dangerous phenomenon occurs, it is important to estimate the probability of certain dynamical behavior of the ship with respect…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
In two previous papers the author described ``Islands of Instability" that may appear in wavefunction models with nonlinear evolution (of a type proposed originally in the context of the Measurement Problem). Such ``IsoI" represent a new…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
Azimuthal instabilities occur in rotationally symmetric systems, either as spinning (rotating) waves or standing waves. We make use of a novel ansatz to derive a differential equation characterizing the state of these instabilities in terms…
This work analyses the dynamical properties of periodically-driven band models. Focusing on the case of Bose-Einstein condensates, and using a meanfield approach to treat inter-particle collisions, we identify the origin of dynamical…
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
In computing ship motion statistics (e.g., exceeding probability) in an irregular wave field, it is a common practice to represent the irregular waves by a large number of wave groups and compute the motion statistics from the distribution…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…
We report an instability exhibited by a fluid system when coupling two distinct types of waves, both linearly damped. While none of them is unstable on its own, they amplify one another, resulting in a previously unreported convective…
We consider the acoustic flow field of rotationally symmetric systems, like an annular combustor and the flow in a round duct, in absence of a mean azimuthal flow field. We focus on azimuthal instabilities, which manifest as either spinning…